In this paper, a new memristor model and a new memcapacitor model are proposed. Based on the two models, a simple chaotic circuit is constructed. Due to the special characteristics of the memristor and memcapacitor, the proposed circuit has two-dimensional normally hyperbolic manifolds of equilibria, and nonparametric bifurcation can occur when the conditions supporting the normal hyperbolicity of such manifolds are not satisfied. By adding a nonlinear controller to the proposed circuit, an anti-controlled system is realized, which has hyperchaotic dynamic behaviors under some suitable control parameters. The stability of equilibrium points and dynamic properties of the original system and the anti-controlled system are explored by Lyapunov exponents, bifurcation diagrams and so on. Furthermore, the anti-controlled system is applied to design a random sequence generator on digital signal processor platform.

中文翻译：

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基于忆阻器-忆电容电路中超混沌的非参数分岔与反控制

本文提出了一种新的忆阻器模型和一种新的忆电容器模型。在这两个模型的基础上，构造了一个简单的混沌电路。由于忆阻器和忆电容器的特殊特性，所提出的电路具有二维正态双曲平衡流形，当支持此类流形的正双曲性的条件不满足时，会发生非参数分岔。通过在所提出的电路中添加非线性控制器，实现了一个反控制系统，该系统在一些合适的控制参数下具有超混沌动态行为。采用李雅普诺夫指数、分岔图等方法探讨了原系统和反受控系统平衡点的稳定性和动力学性质。此外，