Nonparametric Bifurcation and Anti-Control of Hyperchaos in a Memristor-Memcapacitor-Based Circuit

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.

Automated summary

A new memristor and memcapacitor model are proposed in this paper, and a simple chaotic circuit is constructed based on the two models. By adding a nonlinear controller, an anti-controlled system with hyperchaotic dynamic behaviors is realized. The stability and dynamic properties of the original system and the anti-controlled system are explored using Lyapunov exponents and bifurcation diagrams.