A gallery of chaotic systems with an infinite number of equilibrium points

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• 作者：Viet&ndash ; Thanh Pham ; ^a ; ^d ; ^{pvt3010@gmail.com} ; ^{viet-thanh.pham@p.lodz.pl} ; Sajad Jafari^b ; Christos Volos^c ; Tomasz Kapitaniak^d
• 关键词：Chaos ; Hidden attractor ; Equilibrium ; Phase portrait ; Bifurcation diagram ; Lyapunov exponent
• 刊名：Chaos, Solitons & Fractals
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：93
• 期：Complete
• 页码：58-63
• 全文大小：2729 K
• 卷排序：93

文摘

In this work, a systematic search for finding chaotic systems with infinite equilibria is described. As a result, we obtained a gallery of chaotic systems with various shapes of equilibrium points such as a line, two parallel lines, a piece–wise linear curve, a parabola, a hyperbola, or a circle. Interestingly, such novel systems exhibit “hidden attractors”, which play vital roles in nonlinear theory and practical engineering issues.