Zero-Hopf bifurcation and multistability coexistence on a four-neuron network model with multiple delays

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• 作者：Juhong Ge ; Jian Xu ; ZhiQiang Li
• 关键词：Zero ; Hopf singularity ; Multistability coexistence ; Multiple delays
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：87
• 期：4
• 页码：2357-2366
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

In this paper, a four-neuron neural system with four delays is investigated to exhibit the effects of multiple delays and coupled weights on system dynamics. Zero-Hopf bifurcation is obtained, where the system characteristic equation has a simple zero and a simple pair of pure imaginary eigenvalues. The coupled weight and time delay are considered as bifurcation parameters to study dynamical behaviors derived from zero-Hopf bifurcation. Various dynamical behaviors are analyzed near the bifurcation singularity qualitatively and quantitatively in detail by using perturbation- incremental method, and bifurcation diagrams are obtained. Numerical simulations and theoretical results are given to display a stable resting state, multistability coexistence of two resting states and a pair of periodic activities in the neighbor of the zero-Hopf bifurcation point.