D J Mar | PubMed Health

PubMed2001

Phase synchronization of chaotic systems with small phase diffusion.

The geometric theory of phase locking between periodic oscillators is extended to phase coherent chaotic systems. This approach explains the qualitative features of phase locked chaotic systems and provides an analytical tool for a quantitative description of the phase locked states. Moreover, this geometric viewpoint allows us to identify obstructions to phase locking even in systems with negligible phase diffusion, and to provide sufficient conditions for phase locking to occur. We apply these techniques to the Rössler system and a phase coherent electronic circuit and find that numerical results and experiments agree well with theoretical predictions.

Journal Article↗

PubMed1999

Noise shaping in populations of coupled model neurons.

Biological information-processing systems, such as populations of sensory and motor neurons, may use correlations between the firings of individual elements to obtain lower noise levels and a systemwide performance improvement in the dynamic range or the signal-to-noise ratio. Here, we implement such correlations in networks of coupled integrate-and-fire neurons using inhibitory coupling and demonstrate that this can improve the system dynamic range and the signal-to-noise ratio in a population rate code. The improvement can surpass that expected for simple averaging of uncorrelated elements. A theory that predicts the resulting power spectrum is developed in terms of a stochastic point-process model in which the instantaneous population firing rate is modulated by the coupling between elements.

Mathematics↗