Bifurcations and chaos of a discrete-time model in genetic regulatory networks

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• 作者：Dandan Yue ; Zhi-Hong Guan ; Jie Chen ; Guang Ling ; Yonghong Wu
• 关键词：Discrete ; time genetic regulatory network ; Fold bifurcation ; Flip bifurcation ; Neimark–Sacker bifurcation ; Chaos
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：1
• 页码：567-586
• 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, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model.