Chaos

Select this Article FREE

The impact of awareness on epidemic spreading in networks

Qingchu Wu, Xinchu Fu, Michael Small, and Xin-Jian Xu

Chaos 22, 013101 (2012); http://dx.doi.org/10.1063/1.3673573 (8 pages)

Online Publication Date: 3 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We explore the impact of awareness on epidemic spreading through a population represented by a scale-free network. Using a network mean-field approach, a mathematical model for epidemic spreading with awareness reactions is proposed and analyzed. We focus on the role of three forms of awareness including local, global, and contact awareness. By theoretical analysis and simulation, we show that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness can. Also, the influence degree of the local awareness on disease dynamics is closely related with the contact awareness.

+

Show PACS

05.45.-a	Nonlinear dynamics and chaos
87.23.Cc	Population dynamics and ecological pattern formation
89.75.-k	Complex systems

Select this Article

Multiscale dynamics in communities of phase oscillators

Dustin Anderson, Ari Tenzer, Gilad Barlev, Michelle Girvan, Thomas M. Antonsen, and Edward Ott

Chaos 22, 013102 (2012); http://dx.doi.org/10.1063/1.3672513 (12 pages)

Online Publication Date: 3 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We investigate the dynamics of systems of many coupled phase oscillators with heterogeneous frequencies. We suppose that the oscillators occur in M groups. Each oscillator is connected to other oscillators in its group with “attractive” coupling, such that the coupling promotes synchronization within the group. The coupling between oscillators in different groups is “repulsive,” i.e., their oscillation phases repel. To address this problem, we reduce the governing equations to a lower-dimensional form via the ansatz of Ott and Antonsen, Chaos 18, 037113 (2008). We first consider the symmetric case where all group parameters are the same, and the attractive and repulsive coupling are also the same for each of the M groups. We find a manifold math

of neutrally stable equilibria, and we show that all other equilibria are unstable. For M ≥ 3, math

has dimension M − 2, and for M = 2, it has dimension 1. To address the general asymmetric case, we then introduce small deviations from symmetry in the group and coupling parameters. Doing a slow/fast timescale analysis, we obtain slow time evolution equations for the motion of the M groups on the manifold math

. We use these equations to study the dynamics of the groups and compare the results with numerical simulations.

+

Show PACS

05.45.Xt

Synchronization; coupled oscillators

Select this Article

Resonance phenomena and long-term chaotic advection in volume-preserving systems

Dmitri L. Vainchtein and Alimu Abudu

Chaos 22, 013103 (2012); http://dx.doi.org/10.1063/1.3672510 (8 pages)

Online Publication Date: 3 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Creating chaotic advection is the most efficient strategy to achieve mixing on microscale or in very viscous fluids. In this paper, we present a quantitative theory of the long-time resonant mixing in 3D near-integrable flows. We use the flow between two coaxial elliptic counter-rotating cylinders as a demonstrative model, where multiple scatterings on resonance result in mixing by causing the jumps of adiabatic invariants. We improve the existing estimates of the width of the mixing domain. We show that the resulting mixing both on short and long time scales can be described in terms of a single diffusion-type equation with a diffusion coefficient depending on the averaged effect of multiple passages through resonances. We discuss the exact location of the boundaries of the chaotic domain and show how it affects the properties of mixing.

+

Show PACS

47.52.+j	Chaos in fluid dynamics
47.32.Ef	Rotating and swirling flows
47.51.+a	Mixing

Select this Article FREE

Propagation of spiking regularity and double coherence resonance in feedforward networks

Cong Men, Jiang Wang, Ying-Mei Qin, Bin Deng, Kai-Ming Tsang, and Wai-Lok Chan

Chaos 22, 013104 (2012); http://dx.doi.org/10.1063/1.3676067 (7 pages)

Online Publication Date: 10 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We investigate the propagation of spiking regularity in noisy feedforward networks (FFNs) based on FitzHugh-Nagumo neuron model systematically. It is found that noise could modulate the transmission of firing rate and spiking regularity. Noise-induced synchronization and synfire-enhanced coherence resonance are also observed when signals propagate in noisy multilayer networks. It is interesting that double coherence resonance (DCR) with the combination of synaptic input correlation and noise intensity is finally attained after the processing layer by layer in FFNs. Furthermore, inhibitory connections also play essential roles in shaping DCR phenomena. Several properties of the neuronal network such as noise intensity, correlation of synaptic inputs, and inhibitory connections can serve as control parameters in modulating both rate coding and the order of temporal coding.

+

Show PACS

05.45.Xt

Synchronization; coupled oscillators

Select this Article FREE

Transcripts: An algebraic approach to coupled time series

José M. Amigó, Roberto Monetti, Thomas Aschenbrenner, and Wolfram Bunk

Chaos 22, 013105 (2012); http://dx.doi.org/10.1063/1.3673238 (13 pages)

Online Publication Date: 13 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Ordinal symbolic dynamics is based on ordinal patterns. Its tools include permutation entropy (in metric and topological versions), forbidden patterns, and a number of mathematical results that make this sort of symbolic dynamics appealing both for theoreticians and practitioners. In particular, ordinal symbolic dynamics is robust against observational noise and can be implemented with low computational cost, which explains its increasing popularity in time series analysis. In this paper, we study the perhaps less exploited aspect so far of ordinal patterns: their algebraic structure. In a first part, we revisit the concept of transcript between two symbolic representations, generalize it to N representations, and derive some general properties. In a second part, we use transcripts to define two complexity indicators of coupled dynamics. Their performance is tested with numerical and real world data.

+

Show PACS

05.70.Ce	Thermodynamic functions and equations of state
05.45.Tp	Time series analysis
02.40.Re	Algebraic topology
02.60.-x	Numerical approximation and analysis

Select this Article

Saddle-point solutions and grazing bifurcations in an impacting system

Joanna F. Mason and Petri T. Piiroinen

Chaos 22, 013106 (2012); http://dx.doi.org/10.1063/1.3673786 (6 pages)

Online Publication Date: 13 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

This paper focuses on the intricate relationship between smooth and nonsmooth phenomena in an impacting system. In particular a boundary saddle-point solution, that is born in a nonsmooth fold, is analysed. Accessible boundary saddle-point solutions play a key role in determining the global dynamics of a system and here we will show how grazing bifurcations can affect their existence.

+

Show PACS

05.45.-a	Nonlinear dynamics and chaos
45.40.-f	Dynamics and kinematics of rigid bodies

Select this Article

Multiscale characterization of recurrence-based phase space networks constructed from time series

Ruoxi Xiang, Jie Zhang, Xiao-Ke Xu, and Michael Small

Chaos 22, 013107 (2012); http://dx.doi.org/10.1063/1.3673789 (10 pages)

Online Publication Date: 17 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network theory provides a tool to describe either important nodes, or structures that exist in the networks, at different topological scale. This can then provide distinct information for time series of different dynamical systems. In this paper, we systematically investigate the recurrence-based phase space network of order k that has previously been used to specify different types of dynamics in terms of the motif ranking from a different perspective. Globally, we find that the network size scales with different scale exponents and the degree distribution follows a quasi-symmetric bell shape around the value of 2k with different values of degree variance from periodic to chaotic Rössler systems. Local network properties such as the vertex degree, the clustering coefficients and betweenness centrality are found to be sensitive to the local stability of the orbits and hence contain complementary information.

+

Show PACS

89.75.Hc	Networks and genealogical trees
05.45.Tp	Time series analysis
02.50.-r	Probability theory, stochastic processes, and statistics

Select this Article

Fractal variability: An emergent property of complex dissipative systems

Andrew J. E. Seely and Peter Macklem

Chaos 22, 013108 (2012); http://dx.doi.org/10.1063/1.3675622 (7 pages)

Online Publication Date: 19 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

The patterns of variation of physiologic parameters, such as heart and respiratory rate, and their alteration with age and illness have long been under investigation; however, the origin and significance of scale-invariant fractal temporal structures that characterize healthy biologic variability remain unknown. Quite independently, atmospheric and planetary scientists have led breakthroughs in the science of non-equilibrium thermodynamics. In this paper, we aim to provide two novel hypotheses regarding the origin and etiology of both the degree of variability and its fractal properties. In a complex dissipative system, we hypothesize that the degree of variability reflects the adaptability of the system and is proportional to maximum work output possible divided by resting work output. Reductions in maximal work output (and oxygen consumption) or elevation in resting work output (or oxygen consumption) will thus reduce overall degree of variability. Second, we hypothesize that the fractal nature of variability is a self-organizing emergent property of complex dissipative systems, precisely because it enables the system’s ability to optimally dissipate energy gradients and maximize entropy production. In physiologic terms, fractal patterns in space (e.g., fractal vasculature) or time (e.g., cardiopulmonary variability) optimize the ability to deliver oxygen and clear carbon dioxide and waste. Examples of falsifiability are discussed, along with the need to further define necessary boundary conditions. Last, as our focus is bedside utility, potential clinical applications of this understanding are briefly discussed. The hypotheses are clinically relevant and have potential widespread scientific relevance.

+

Show PACS

87.19.Wx

Pneumodyamics, respiration

Select this Article

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Bartolo Luque, Lucas Lacasa, Fernando J. Ballesteros, and Alberto Robledo

Chaos 22, 013109 (2012); http://dx.doi.org/10.1063/1.3676686 (14 pages)

Online Publication Date: 24 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

+

Show PACS

05.45.Tp	Time series analysis
05.70.Ce	Thermodynamic functions and equations of state
02.20.Bb	General structures of groups
02.30.Oz	Bifurcation theory
02.60.Pn	Numerical optimization

Select this Article

Theoretical analysis of multiplicative-noise-induced complete synchronization in global coupled dynamical network

Yuzhu Xiao, Sufang Tang, and Yong Xu

Chaos 22, 013110 (2012); http://dx.doi.org/10.1063/1.3677253 (7 pages)

Online Publication Date: 24 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

In this paper, based on the theory of stochastic differential equation, we study the effect of noise on the synchronization of global coupled dynamical network, when noise presents in coupling term. The theoretical result shows that noise can really induce synchronization. To verify the theoretical result, Cellular Neural Network neural model and Rössler-like system are performed as numerical examples.

+

Show PACS

05.45.Xt	Synchronization; coupled oscillators
05.90.+m	Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
02.30.Hq	Ordinary differential equations
02.50.Ey	Stochastic processes
02.60.Lj	Ordinary and partial differential equations; boundary value problems
05.10.Gg	Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

Select this Article Author Select

Using time-delayed mutual information to discover and interpret temporal correlation structure in complex populations

D. J. Albers and George Hripcsak

Chaos 22, 013111 (2012); http://dx.doi.org/10.1063/1.3675621 (25 pages)

Online Publication Date: 24 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

This paper addresses how to calculate and interpret the time-delayed mutual information (TDMI) for a complex, diversely and sparsely measured, possibly non-stationary population of time-series of unknown composition and origin. The primary vehicle used for this analysis is a comparison between the time-delayed mutual information averaged over the population and the time-delayed mutual information of an aggregated population (here, aggregation implies the population is conjoined before any statistical estimates are implemented). Through the use of information theoretic tools, a sequence of practically implementable calculations are detailed that allow for the average and aggregate time-delayed mutual information to be interpreted. Moreover, these calculations can also be used to understand the degree of homo or heterogeneity present in the population. To demonstrate that the proposed methods can be used in nearly any situation, the methods are applied and demonstrated on the time series of glucose measurements from two different subpopulations of individuals from the Columbia University Medical Center electronic health record repository, revealing a picture of the composition of the population as well as physiological features.

+

Show PACS

05.45.Tp	Time series analysis
02.50.-r	Probability theory, stochastic processes, and statistics

Select this Article

Vibrational resonance in Duffing systems with fractional-order damping

J. H. Yang and H. Zhu

Chaos 22, 013112 (2012); http://dx.doi.org/10.1063/1.3678788 (9 pages)

Online Publication Date: 27 January 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

The phenomenon of vibrational resonance (VR) is investigated in over- and under-damped Duffing systems with fractional-order damping. It is found that the factional-order damping can induce change in the number of the steady stable states and then lead to single- or double-resonance behavior. Compared with vibrational resonance in the ordinary systems, the following new results are found in the fractional-order systems. (1) In the overdamped system with double-well potential and ordinary damping, there is only one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for these new resonance behaviors is the value of the fractional-order satisfies α > 1. (2) In the overdamped system with single-well potential and ordinary damping, there is no resonance, whereas there is a single-resonance for the case of fractional-order damping. The necessary condition for the new result is α > 1. (3) In the underdamped system with double-well potential and ordinary damping, there are double-resonance and one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for the new single-resonance is α < 1. (4) In the underdamped system with single-well potential, there is at most a single-resonance existing for both the cases of ordinary and fractional-order damping. In the underdamped systems, varying the value of the fractional-order is equivalent to change the damping parameter for some cases.

+

Show PACS

05.45.-a

Nonlinear dynamics and chaos

Select this Article

Symmetry chaotic attractors and bursting dynamics of semiconductor lasers subjected to optical injection

A. D. Mengue and B. Z. Essimbi

Chaos 22, 013113 (2012); http://dx.doi.org/10.1063/1.3675623 (10 pages)

Online Publication Date: 1 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

This paper presents the nonlinear dynamics and bifurcations of optically injected semiconductor lasers in the frame of relative high injection strength. The behavior of the system is explored by means of bifurcation diagrams; however, the exact nature of the involved dynamics is well described by a detailed study of the dynamics evolutions as a function of the effective gain coefficient. As results, we notice the different types of symmetry chaotic attractors with the riddled basins, supercritical pitchfork and Hopf bifurcations, crisis of attractors, instability of chaos, symmetry breaking and restoring bifurcations, and the phenomena of the bursting behavior as well as two connected parts of the same chaotic attractor which merge in a periodic orbit.

+

Show PACS

05.45.-a

Nonlinear dynamics and chaos

Select this Article

Multistability of twisted states in non-locally coupled Kuramoto-type models

Taras Girnyk, Martin Hasler, and Yuriy Maistrenko

Chaos 22, 013114 (2012); http://dx.doi.org/10.1063/1.3677365 (10 pages)

Online Publication Date: 2 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without the limitation of the generality, the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type, and therefore, all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2πq/N, are equilibrium points, where q is an integer. Their stability in the limit N → ∞ is discussed along the line of Wiley et al. [Chaos 16, 015103 (2006)] In addition, we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2πq/N in one sector of the ring, −2πq/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N → ∞. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points, and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N → ∞.

+

Show PACS

05.45.Xt	Synchronization; coupled oscillators
02.60.-x	Numerical approximation and analysis

Select this Article

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Yong Zou, Reik V. Donner, and Jürgen Kurths

Chaos 22, 013115 (2012); http://dx.doi.org/10.1063/1.3677367 (12 pages)

Online Publication Date: 2 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

+

Show PACS

05.45.Tp	Time series analysis
02.50.-r	Probability theory, stochastic processes, and statistics
02.60.-x	Numerical approximation and analysis

Select this Article

Long-range interactions between adjacent and distant bases in a DNA and their impact on the ribonucleic acid polymerase-DNA dynamics

M. Saha and T. C. Kofane

Chaos 22, 013116 (2012); http://dx.doi.org/10.1063/1.3683430 (12 pages)

Online Publication Date: 14 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physiological temperature, we propose a spin-like model of DNA nonlinear dynamics with long-range interactions (LRI) between adjacent and distant base pairs to study RNAP-DNA dynamics. Using Holstein-Primakoff’s representation and Glauber’s coherent state representation, we show that the model equation is a completely integrable nonlinear Schrödinger equation whose dispersive coefficient depends on LRI’s parameter. Inhomogeneities have introduced perturbation terms in the equation of motion of RNAP-DNA dynamics. Considering the homogeneous part of that equation, a detailed study of the solution shows that the number of base pairs which form the bubble, the height, and the width of that bubble depend on the long-range parameter. The results of the perturbation analysis show that the inhomogeneities due to the DNA and RNAP structures do not alter the velocity and amplitude of the soliton, but introduce some fluctuations in the localized region of the soliton. The events that happen in the present study may represent binding of an RNAP to a promoter site in the DNA during the transcription process.

+

Show PACS

87.15.hg	Dynamics of intermolecular interactions
87.14.gn	RNA
87.14.gk	DNA

Select this Article

The structure and resilience of financial market networks

Thomas Kauê Dal’Maso Peron, Luciano da Fontoura Costa, and Francisco A. Rodrigues

Chaos 22, 013117 (2012); http://dx.doi.org/10.1063/1.3683467 (6 pages)

Online Publication Date: 14 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Financial markets can be viewed as a highly complex evolving system that is very sensitive to economic instabilities. The complex organization of the market can be represented in a suitable fashion in terms of complex networks, which can be constructed from stock prices such that each pair of stocks is connected by a weighted edge that encodes the distance between them. In this work, we propose an approach to analyze the topological and dynamic evolution of financial networks based on the stock correlation matrices. An entropy-related measurement is adopted to quantify the robustness of the evolving financial market organization. It is verified that the network topological organization suffers strong variation during financial instabilities and the networks in such periods become less robust. A statistical robust regression model is proposed to quantity the relationship between the network structure and resilience. The obtained coefficients of such model indicate that the average shortest path length is the measurement most related to network resilience coefficient. This result indicates that a collective behavior is observed between stocks during financial crisis. More specifically, stocks tend to synchronize their price evolution, leading to a high correlation between pair of stock prices, which contributes to the increase in distance between them and, consequently, decrease the network resilience.

+

Show PACS

89.65.Gh	Economics; econophysics, financial markets, business and management
02.50.-r	Probability theory, stochastic processes, and statistics
89.75.Hc	Networks and genealogical trees

Select this Article

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling

G. Sigalov, O. V. Gendelman, M. A. AL-Shudeifat, L. I. Manevitch, A. F. Vakakis, and L. A. Bergman

Chaos 22, 013118 (2012); http://dx.doi.org/10.1063/1.3683480 (10 pages)

Online Publication Date: 14 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

+

Show PACS

05.45.Pq

Numerical simulations of chaotic systems

Select this Article

Finger tapping movements of Parkinson’s disease patients automatically rated using nonlinear delay differential equations

C. Lainscsek, P. Rowat, L. Schettino, D. Lee, D. Song, C. Letellier, and H. Poizner

Chaos 22, 013119 (2012); http://dx.doi.org/10.1063/1.3683444 (13 pages)

Online Publication Date: 16 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Parkinson’s disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson’s patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson’s patients and controls. The algorithmic scores compared favorably with the unified Parkinson’s disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p<0.0015) correlation between them.

+

Show PACS

87.19.X-	Diseases
02.60.-x	Numerical approximation and analysis
02.50.-r	Probability theory, stochastic processes, and statistics
87.85.G-	Biomechanics

Select this Article

Stabilization of chaos systems described by nonlinear fractional-order polytopic differential inclusion

Saeed Balochian and Ali Khaki Sedigh

Chaos 22, 013120 (2012); http://dx.doi.org/10.1063/1.3683487 (8 pages)

Online Publication Date: 16 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

In this paper, sliding mode control is utilized for stabilization of a particular class of nonlinear polytopic differential inclusion systems with fractional-order-0 < q < 1. This class of fractional order differential inclusion systems is used to model physical chaotic fractional order Chen and Lu systems. By defining a sliding surface with fractional integral formula, exploiting the concept of the state space norm, and obtaining sufficient conditions for stability of the sliding surface, a special feedback law is presented which enables the system states to reach the sliding surface and consequently creates a sliding mode control. Finally, simulation results are used to illustrate the effectiveness of the proposed method.

+

Show PACS

05.45.Gg	Control of chaos, applications of chaos
02.60.Lj	Ordinary and partial differential equations; boundary value problems

Select this Article

Bifurcation phenomena in an impulsive model of non-basal testosterone regulation

Zhanybai T. Zhusubaliyev, Alexander N. Churilov, and Alexander Medvedev

Chaos 22, 013121 (2012); http://dx.doi.org/10.1063/1.3685519 (11 pages)

Online Publication Date: 23 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Complex nonlinear dynamics in a recent mathematical model of non-basal testosterone regulation are investigated. In agreement with biological evidence, the pulsatile (non-basal) secretion of testosterone is modeled by frequency and amplitude modulated feedback. It is shown that, in addition to already known periodic motions with one and two pulses in the least period of a closed-loop system solution, cycles of higher periodicity and chaos are present in the model in hand. The broad range of exhibited dynamic behaviors makes the model highly promising in model-based signal processing of hormone data.

+

Show PACS

87.19.rh	Fluid transport and rheology
47.52.+j	Chaos in fluid dynamics
05.45.-a	Nonlinear dynamics and chaos

Select this Article

Neural networks and chaos: Construction, evaluation of chaotic networks, and prediction of chaos with multilayer feedforward networks

Jacques M. Bahi, Jean-François Couchot, Christophe Guyeux, and Michel Salomon

Chaos 22, 013122 (2012); http://dx.doi.org/10.1063/1.3685524 (9 pages)

Online Publication Date: 23 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now, these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish, based on a rigorous theoretical framework, an equivalence between chaotic iterations according to Devaney and a particular class of neural networks. On the one hand, we show how to build such a network, on the other hand, we provide a method to check if a neural network is a chaotic one. Finally, the ability of classical feedforward multilayer perceptrons to learn sets of data obtained from a dynamical system is regarded. Various boolean functions are iterated on finite states. Iterations of some of them are proven to be chaotic as it is defined by Devaney. In that context, important differences occur in the training process, establishing with various neural networks that chaotic behaviors are far more difficult to learn.

+

Show PACS

07.05.Mh	Neural networks, fuzzy logic, artificial intelligence
02.10.-v	Logic, set theory, and algebra

Select this Article

Nonlinear dynamics of the membrane potential of a bursting pacemaker cell

J. M. González-Miranda

Chaos 22, 013123 (2012); http://dx.doi.org/10.1063/1.3687017 (12 pages)

Online Publication Date: 23 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

This article presents the results of an exploration of one two-parameter space of the Chay model of a cell excitable membrane. There are two main regions: a peripheral one, where the system dynamics will relax to an equilibrium point, and a central one where the expected dynamics is oscillatory. In the second region, we observe a variety of self-sustained oscillations including periodic oscillation, as well as bursting dynamics of different types. These oscillatory dynamics can be observed as periodic oscillations with different periodicities, and in some cases, as chaotic dynamics. These results, when displayed in bifurcation diagrams, result in complex bifurcation structures, which have been suggested as relevant to understand biological cell signaling.

+

Show PACS

87.16.dp	Transport, including channels, pores, and lateral diffusion
87.16.Vy	Ion channels
87.16.A-	Theory, modeling, and simulations

Select this Article

Exponential synchronization of stochastic neural networks with leakage delay and reaction-diffusion terms via periodically intermittent control

Qintao Gan

Chaos 22, 013124 (2012); http://dx.doi.org/10.1063/1.3685523 (10 pages)

Online Publication Date: 24 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We explore the issue of integrating leakage delay, stochastic noise perturbation, and reaction-diffusion effects into the study of synchronization for neural networks with time-varying delays. By using Lyapunov stability theory and stochastic analysis approaches, a periodically intermittent controller is proposed to guarantee the exponential synchronization of proposed coupled neural networks based on p-norm. Some existing results are improved and extended. The usefulness and superiority of our theoretical results are illustrated by a numerical example.

+

Show PACS

02.30.Yy	Control theory
05.45.Xt	Synchronization; coupled oscillators
89.20.Kk	Engineering

Select this Article

Conedy: A scientific tool to investigate complex network dynamics

Alexander Rothkegel and Klaus Lehnertz

Chaos 22, 013125 (2012); http://dx.doi.org/10.1063/1.3685527 (8 pages)

Online Publication Date: 28 February 2012

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We present Conedy, a performant scientific tool to numerically investigate dynamics on complex networks. Conedy allows to create networks and provides automatic code generation and compilation to ensure performant treatment of arbitrary node dynamics. Conedy can be interfaced via an internal script interpreter or via a Python module.

+

Show PACS