Abstract
In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.
Highlights
Memristor was first proposed by Chua [1] in 1971 and is the fourth basic electronic component manufactured by HP Labs in 2008 [2]. e discovery of memristors has caused an upsurge in studying and applying memristors
Due to the nonlinearity of memristor, it has been applied in many fields, such as flash memory [2, 3], neuromorphic computing [4, 5], neural network [6, 7], and chaotic system [8,9,10,11] based on chaos synchronization for encryption algorithms [12, 13] and secure communication [14, 15]
In 2017, a multiscroll hyperchaotic system was proposed by introducing the memristor into the jerk multiscroll system, and the numbers of scrolls can be controlled by adjusting the coefficient before the term related to memristor [19]
Summary
Memristor was first proposed by Chua [1] in 1971 and is the fourth basic electronic component manufactured by HP Labs in 2008 [2]. e discovery of memristors has caused an upsurge in studying and applying memristors. A memristor-based chaotic system is constructed by introducing an ideal flux-controlled memristor with absolute value nonlinearity into an existing hypogenetic chaotic jerk system, which can exhibit the extreme multistability phenomenon in reference [31]. A simplest third-order memristive chaotic system with hidden attractors is proposed, which exhibits the extreme multistability phenomenon of coexisting infinitely many attractors in reference [32]. The presented memristor-based system displays other complex dynamic characteristics, including constant Lyapunov exponents, discrete bifurcation diagrams, the symmetry of coexisting attractors, and so on.
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