Spike synchronization of chaotic oscillators as a phase transition

Abstract

We study how a locally coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of synchronization is called a defect. The system displays sudden spontaneous defect disappearance at a critical coupling strength suggesting an existence of a phase transition. Below critical coupling, the system reaches order at a definite amplitude of an external input; this order persists for a fixed time slot. Thus, the array behaves as an excitable-like system, even though the single element lacks such a property.

Exploring the Kibble–zurek Mechanism in a Secondary Bifurcation

“…In this sense, this work is very relevant because the results on the quenched dynamics in the critical region can be translated into the interaction and collective behavior of those oscillators. Notwithstanding the existence of very few numerical works [53] pointing towards this direction.…”

Comparison of single neuron models in terms of synchronization propensity

“…The property of excitability can emerge as a collective one, by coupling nonexcitable, but HC, individual elements; this matter is dealt with extensively in another paper. 42 We conclude with some comparisons between chaotic and excitable dynamics as possible models for single neurons. Reference 31 deals with excitable systems ruled by only two coupled ͑fast and slow͒ equations.…”