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arXiv · 1501.07799

Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators

Farzad Farkhooi·Carl van Vreeswijk
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Abstract

We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of inter-event density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework, can readily be extended to the analysis of systems with more state variables. To exhibit this, we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate stability of this system and we show it undergoes a super-critical Hopf bifurcation to collective synchronization.

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Farzad Farkhooi, Carl van Vreeswijk. 2015-01-30. Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators. https://doi.org/10.1103/physrevlett.115.038103

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