A novel non-equilibrium memristor-based system with multi-wing attractors and multiple transient transitions

Abstract

Based on the pure mathematical model of the memristor, this paper proposes a novel memristor-based chaotic system without equilibrium points. By selecting different parameters and initial conditions, the system shows extremely diverse forms of winglike attractors, such as period-1 to period-12 wings, chaotic single-wing, and chaotic double-wing attractors. It was found that the attractor basins with three different sets of parameters are interwoven in a complex manner within the relatively large (but not the entire) initial phase plane. This means that small perturbations in the initial conditions in the mixing region will lead to the production of hidden extreme multistability. At the same time, these sieve-shaped basins are confirmed by the uncertainty exponent. Additionally, in the case of fixed parameters, when different initial values are chosen, the system exhibits a variety of coexisting transient transition behaviors. These 14 were also where the same state transition from period 18 to period 18 was first discovered. The above dynamical behavior is analyzed in detail through time-domain waveforms, phase diagrams, attraction basin, bifurcation diagrams, and Lyapunov exponent spectrum . Finally, the circuit implementation based on the digital signal processor verifies the numerical simulation and theoretical analysis.

Generating novel multi-scroll chaotic attractors via fractal transformation

“…In 2021, Jahanshahi et al discussed a four-dimensional system with hidden attractors that lacks equilibria [18]. Gu et al also discovered a novel non-equilibrium memristor-based system with multi-wing attractors and multiple transient transitions [19]. Motivated by research literatures on chaotic systems with hidden attractors, we present a novel non-equilibrium point chaotic system in this paper.…”

Odd and Even Functions in the Design Problem of New Chaotic Attractors

“…One such direction is the creation of chaotic memristor systems. For example, in article [Gu et al, 2021], a memristor system without equilibrium positions was considered; in [Liu et al, 2019], a memristor was used to increase the complexity of the system, and in [Lai et al, 2020a], a new memristor system was constructed from a Lorenz-type system.…”