Double memristors oscillator with hidden stacked attractors and its multi-transient and multistability analysis. (July 2021)

• Record Type: Journal Article
• Authors: Du, Chuanhong; Liu, Licai; Zhang, Zhengping; Yu, Shixing
• Is Part Of: Chaos, solitons and fractals. Volume 148(2021)
• Publication Date: 2021-07
• Subjects: Stacked attractor -- Double memristors -- Chaos -- Multi-transient phenomenon -- Quasi-periodic multistability; 00-01 -- 99-00; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111023
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: An oscillator composed of two different types of memristors having a novel hidden stacked attractor. Simple analog circuit structure for the oscillator. Having the phenomenon of multi transient. Having quasi-periodic multist ability behaviors. The dynamic characteristics of the oscillator were verified experimentally using a DSP platform. Abstract: In this paper, by replacing the two linear resistors in the RLC oscillator with flux-controlled and charge-controlled memristors, a novel double memristors nonlinear circuit system is proposed. From the oscillator circuit, we established the mathematical model of the system and proved that it is a hidden system without equilibrium. The numerical simulation results of the mathematical model are consistent with the circuit. What is more, we also find that one state variable of the system has the typical slow change behavior, which is reflected in the form of step-like or square-like waves, thus forming a novel stacked attractor. Then, through studying the Poincaré map, phase diagram, bifurcation diagram, Lyapunov exponents (LEs), it was proved that the system has multi-transient behaviors such as chaos to another chaos, chaos to period, chaos to quasi-period, quasi-period to period. Besides, the memristive oscillator has quasi-periodic multistability when changing the initial values, which is a rare phenomenon for a chaotic system. These findings indicate that the proposed memristive hidden oscillator has complex nonlinear dynamic characteristics. Finally, the Digital Signal Processing (DSP) hardware platform confirms the physical realizability of the oscillator, offering the possibility of engineering applications.