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Research Highlight Archive
The compass rose pattern in electricity prices
Jonathan A. Batten and Mahmoud Hamada
The “compass rose pattern” is known to appear in the phase portraits, or scatter diagrams, of the high-frequency returns of financial series. It is shown that this pattern is also present in the returns of spot electricity prices.
Frozen state of spiral waves in excitable media
Jinming Luo, Bingsheng Zhang, and Meng Zhan
Frozen state of spiral waves can spontaneously appear in both excitable and oscillatory media, in which several spiral waves coexist and are well separated by thin walls (shocks). This work studies the global structure of frozen state of spiral waves in excitable media and finds that, different from stationary shocks in oscillatory media, in excitable media the shock dynamics actually depends on the status of single spiral.
A "cellular neuronal" approach to optimization problems
Gregory S. Duane
The Hopfield–Tank recurrent neural network architecture for the traveling salesman problem is generalized to a fully interconnected “cellular” neural network of regular oscillators. Tours are defined by synchronization patterns, allowing the simultaneous representation of all cyclic permutations of a given tour. The network converges to local optima some of which correspond to shortest-distance tours, as can be shown analytically in a stationary phase approximation. Simulated annealing is required for global optimization, but the stochastic element might be replaced by chaotic intermittency in a further generalization of the architecture to a network of chaotic oscillators.
On the dynamics of chaotic spiking-bursting transition in the Hindmarsh–Rose neuron
G. Innocenti and R. Genesio
The Hindmarsh-Rose model, a three-dimensional oscillator model, aimed to study the spiking-bursting behavior of the neuron membrane potential is examined and the system dynamics which control transition between the spiking and bursting regimes is studied in detail.
Recurrences determine the dynamics
G. Robinson and M. Thiel
This paper proves a theorem that shows that recurrences are not only an important characteristic of a dynamical system but that—if properly used—they determine the dynamics of a system completely. Therefore, they yield an alternative description of a system’s dynamics. The theorem also provides a mathematical foundation for frequently used methods of data analysis, e.g., recurrence plots, surrogate data methods, and synchronization analysis. The theorem, however, is not limited to the realm of dynamical systems. Relevance to topology is also discussed.
Automated synchrogram analysis applied to heartbeat and reconstructed respiration
Claudia Hamann, Ronny P. Bartsch, Aicko Y. Schumann, Thomas Penzel, Shlomo Havlin, and Jan W. Kantelhardt
A review of the authors’ study of phase synchronization between heartbeat and respiration during sleep using an automated procedure for screening the synchrograms is presented. It is found that synchronization is enhanced during non-REM sleep and reduced during REM sleep.
Nonlinear analysis and modeling of cortical activation and deactivation patterns in the immature fetal ECoG
Karin Schwab, Tobias Groh, Matthias Schwab, and Herbert Witte
An approach combining time-continuous nonlinear stability analysis and a parametric bispectral method was introduced to better describe cortical activation and deactivation patterns in the immature fetal EEG. A combined nonlinear and time-variant approach was able to provide important insights into the properties of the immature fetal ECoG.
