Coexisting attractors in a memcapacitor-based chaotic oscillator

Abstract

In this paper, a smooth curve model of memcapacitor and its equivalent circuit are designed. Based on this memcapacitor, a novel memcapacitive chaotic circuit is presented. Dynamical behaviors of the circuit with various parameters are investigated both theoretically and experimentally. The numerical results indicate that the circuit displays complex nonlinear properties including coexisting and symmetrical bifurcations. The main characteristic of this memcapacitive chaotic circuit is the various coexisting attractors. Different kinds of coexisting attractors and their corresponding conditions are given. The equilibrium set, Lyapunov exponent spectrum and the basin of attraction are also analyzed. Besides, experimental results are given to confirm the correction of the numerical simulations.

A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes

“…On the other hand, coexisting chaotic attractors have been reported in many nonlinear systems in the recent years [19][20][21][22][23]. In [20,21], the coexisting chaotic attractors were found in some 4D smooth systems, and there are overlaps between the coexisting chaotic attractors.…”

“…In [20,21], the coexisting chaotic attractors were found in some 4D smooth systems, and there are overlaps between the coexisting chaotic attractors. In [22], Kengne et al reported a simple 3D autonomous jerk system with multiple attractors; the chaotic system in [22] belongs to the generalized Lü chaotic system family.…”

A Fractional‐Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

“…There are overlaps between the coexisting chaotic attractors in [3][4][5][7][8][9]. However, there are two isolated chaotic attractors in fractional-order chaotic system (2); that is, there are no overlaps between the coexisting chaotic attractors in fractional-order chaotic system (2).…”

“…The high irregularity, unpredictability, and complexity in chaotic systems [1,2] have been widely used in the field of engineering and technology such as secure communications, image steganography, authenticated encryption, motor control, and power system protection. Recently, coexisting chaotic attractors have been found in chaotic systems [3][4][5][6][7][8][9]. For example, the coexisting chaotic attractors in a 3D no-equilibrium system were reported by Pham et al [3], the coexisting multiple attractors in Hopfield neural network were found by Bao et al [4], the coexisting chaotic attractors in a hyperchaotic hyperjerk system were given by Wang et al [5], the coexisting "positive attractor" and "negative attractor" in a 3D autonomous continuous chaotic system were found by Zhou and Ke [6], and so on [7][8][9].…”

Coexisting Oscillation and Extreme Multistability for a Memcapacitor‐Based Circuit

“…So several memcapacitor models, including piecewise linear, quadric and cubic function models, memristor-based memcapacitor models, and memcapacitor emulators, were proposed in [16][17][18][19][20][21], and a mathematical memcapacitor model and a corresponding circuit model are established in [22]. Some special phenomena such as hidden attractors, coexistence attractors, and extreme multistability were found in memcapacitorbased chaotic oscillators [23,24] and memristor-based chaotic oscillators [25][26][27]. In fact, multistability and coexisting attractors have caught the attention of researcher in general chaotic systems [28][29][30].…”