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.

Chaos 19, 043106 (2009)

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.

Chaos 19, 033133 (2009)

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.

Chaos 19, 033114 (2009)

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.

Chaos 19, 023124 (2009)