Abstract
By introducing an ideal and active flux-controlled memristor and tangent function into an existing chaotic system, an interesting memristor-based self-replication chaotic system is proposed. The most striking feature is that this system has infinite line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. In this paper, bifurcation diagrams and Lyapunov exponential spectrum are used to analyze in detail the influence of various parameter changes on the dynamic behavior of the system; it shows that the newly proposed chaotic system has the phenomenon of alternating chaos and limit cycle. Especially, transition behavior of the transient period with steady chaos can be also found for some initial conditions. Moreover, a hardware circuit is designed by PSpice and fabricated, and its experimental results effectively verify the truth of extreme multistability.
Highlights
In 1963, the first chaotic system was discovered by Lorenz
Due to the introduction of the ideal memristor [11–16], the dynamic system based on the memristor produces infinite equilibria, such as line equilibria and surface equilibria. ese equilibria are related to the initial state variables of the memristor. ese memristor models exhibit complex chaotic behaviors and produce multistability phenomena [17, 18]
Bao et al [22] introduced an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system, an interesting memristor-based chaotic system with a hypogenetic jerk equation, and proposed circuit forms. e most striking feature is that this system has four line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors
Summary
In 1963, the first chaotic system was discovered by Lorenz. Since many scientists have constructed many new chaotic systems, such as Chen system, Lu system, and Jerk system [1, 2]. en, in 1971, Chua proposed the memristor, the fourth element after resistor [3, 4], capacitor, and inductor. Ese memristor models exhibit complex chaotic behaviors and produce multistability phenomena [17, 18]. E most striking feature is that this system has four line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. Inspired by the abovementioned ideas, an interesting memristor-based chaotic system is constructed in this paper, which is achieved by introducing a tangent function (tan(z)) and an ideal and active flux-controlled memristor with absolute value nonlinearity into an existing chaotic system boostable VB18 [31]. E newly proposed memristive system has infinite line equilibria and can exhibit the initialcondition-dependent extreme multistablity phenomenon of coexisting infinitely many attractors, which has seldom been reported in the academic literature.
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