DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS

被引：3

作者：

Jiang, Can ^{[1
]}

Guo, Shangjiang ^{[1
]}

He, Yigang ^{[2
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] Hunan Univ, Coll Elect & Informat Engn, Changsha 410082, Hunan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2011年 / 21卷 / 03期

关键词：

Bifurcation; neural network; time delay; periodic solutions; stability; HOPF-BIFURCATION ANALYSIS; BAM NEURAL-NETWORK; NONLINEAR-WAVES; RING NETWORK; DIFFERENTIAL-EQUATIONS; INHIBITORY CONNECTION; PATTERN-FORMATION; IDENTICAL CELLS; NEURONS; STABILITY;

D O I：

10.1142/S0218127411028787

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A model of time-delay recurrently coupled spatially segregated neural oscillators is proposed. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. Bifurcation analysis shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multi-stability, hysteresis, and stability switches of the rest state provoked by the time delay as well as the strength of the connections between the oscillators. Then we derive the equation describing the flow on the center manifold that enables us to determine the bifurcation direction and stability of bifurcated periodic solutions and equilibria. We also give some numerical simulations to support our main results.

引用

页码：775 / 788

页数：14

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