Bifurcation Analysis of a Network of Three Neurons with Time Delays
The paper studies the dynamical behaviors of a recurrent neural network model consisting of three neurons with time delays through theoretical analysis and numerical simulations. The local stability of the trivial equilibrium of the network is analyzed and the sufficient conditions of the existence of Hopf bifurcation are given by discussing the associated characteristic equation. The direction and stability of the bifurcated periodic oscillations arising from Hopf bifurcation, which depend on the nonlinear terms of the network, are determined by means of the normal form and the center manifold theorem. Afterwards, numerical examples are performed to validate the theoretical analysis. The case studies of numerical simulations reach nice agreement with the theoretical results.
Recurrent neural networks Time delay Stability Periodic oscillations
Xiaochen Mao
Department of Engineering Mechanics, Hohai University, Nanjing, China
国际会议
上海
英文
147-150
2011-10-21（万方平台首次上网日期，不代表论文的发表时间）