From Memristor-Modeled Jerk System to the Nonlinear Systems with Memristor

• Published in: Symmetry (Basel) Vol. 14; no. 4; p. 659
• Main Authors: Wu, Xianming, He, Shaobo, Tan, Weijie, Wang, Huihai
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-04-2022
• Subjects: chaos; Circuits; complexity; Equilibrium; Hysteresis loops; jerk system; Liapunov exponents; Lorenz system; Mathematical models; memristor; Memristors; Nonlinear systems; symmetry; Variables
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym14040659

Based on the proposed generalized memristor, a new jerk system is proposed. The complex dynamics of the system are investigated by means of bifurcation diagrams, Lyapunov exponents, and MSampEn, and rich dynamics are observed. Moreover, the circuits of the generalized memristor and the jerk system are physically implemented in the hardware level. The experimental results show that the memristor circuit can generate “8”-shaped pinched hysteresis loops, and the observed attractors match well with the numerical simulations results. In this paper, we summarize nonlinear systems with memristors in the references. It indicates that there are two symmetry methods to find a memristor model in nonlinear systems. However, some of them cannot be realized using the memristor devices, although a memristor model can be found. For example, the famous Lorenz system contains a memristor function, but it cannot be realized using the memristor device. The principles regarding whether nonlinear systems with a memristor function can be realized using a memristor device are discussed.