A simple chaotic system with non-hyperbolic equilibria

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• 作者：Chun-Lai Li^a ; ^{ChaoEncryption@126.com" class="auth_mail" title="E-mail the corresponding author} ; ^{hnistlichl@163.com" class="auth_mail" title="E-mail the corresponding author} ; Jian-Bin Xiong^b
• 关键词：&Scaron ; il&rsquo ; nikov sense chaos ; Dynamical behavior ; Non-hyperbolic equilibrium
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：128
• 期：Complete
• 页码：42-49
• 全文大小：2061 K

文摘

This paper constructs a three-dimensional autonomous chaotic system with simple algebraic structure of only five terms. Interestingly, this system is found to possess two non-hyperbolic equilibria, thus it is not under the class of Šil’nikov sense chaos for owning neither heteroclinic orbit nor homoclinic orbit. Dynamical properties have been revealed with the help of bifurcation route, Poincaré map, frequency spectrum, amplitude modulation and topological horseshoe. We hope that our work can motivate a stimulus for the further study on non-Šil’nikov chaotic system with non-hyperbolic equilibrium.