On the Number of Coexisting Autowaves in the Chain of Coupled Oscillators

Abstract

We consider a model of neuron complex formed by a chain of diffusion coupled oscillators. Every oscillator simulates a separate neuron and is given by a singularly perturbed nonlinear differential-difference equation with two delays. Oscillator singularity allows reduction to limit system without small parameters but with pulse external action. The statement on correspondence between the resulting system with pulse external action and the original oscillator chain gives a way to demonstrate that under consistent growth of the chain node number and decrease of diffusion coefficient we can obtain in this chain unlimited growth of its coexistent stable periodic orbits (buffer phenomenon). Numerical simulations give the actual dependence of the number of stable orbits on the diffusion parameter value.

Keywords

• дифференциально-разностные уравнения
• релаксационный цикл
• автоволны
• устойчивость
• буферность
• bursting-эффект