A model in a coupled system of simple neural oscillators with delays

Authors:
Chunrui Zhang;Yazhuo Zhang;Baodong Zheng
Affiliations:
Department of Mathematics, Northeast Forestry University, Harbin 150040, PR China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 4
Cited 1

Elements of applied bifurcation theory (2nd ed.)

Elements of applied bifurcation theory (2nd ed.)
Theory and applications of Hopf bifurcations in symmetric functional differential equations

Nonlinear Analysis: Theory, Methods & Applications
Hopf bifurcation in bidirectional associative memory neural networks with delays: analysis and computation

Journal of Computational and Applied Mathematics
Specific locking in populations dynamics: Symmetry analysis for coupled heteroclinic cycles

Journal of Computational and Applied Mathematics

Three cell symmetry discrete-time-delayed neural network

Neurocomputing

Quantified Score

Hi-index	7.29

Visualization

Abstract

We consider a coupled system of simple neural oscillators. Using the symmetric functional differential equation theories of Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Transactions of the American Mathematical Society 350 (12) (1998) 4799-4838], we demonstrate the multiple Hopf bifurcations of the equilibrium at the origin. The existence of multiple branches of bifurcating periodic solution is obtained. Then some numerical simulations support our analysis results.