Abstract
Memristor-based systems can exhibit the phenomenon of extreme multi-stability, which results in the coexistence of infinitely many attractors. However, most of the recently published literature focuses on the extreme multi-stability related to memristor initial conditions rather than non-memristor initial conditions. In this paper, we present a new five-dimensional (5-D) two-memristor-based jerk (TMJ) system and study complex dynamical effects induced by memristor and non-memristor initial conditions therein. Using multiple numerical methods, coupling-coefficient-reliant dynamical behaviors under different memristor initial conditions are disclosed, and the dynamical effects of the memristor initial conditions under different non-memristor initial conditions are revealed. The numerical results show that the dynamical behaviors of the 5-D TMJ system are not only dependent on the coupling coefficients, but also dependent on the memristor and non-memristor initial conditions. In addition, with the analog and digital implementations of the 5-D TMJ system, PSIM circuit simulations and microcontroller-based hardware experiments validate the numerical results.
Highlights
A nonlinear dynamical system can exhibit chaotic dynamics for specific system parameters and initial conditions [1,2]
Most of the recently published literature only focuses on the extreme multi-stability related to the initial conditions of memristors [35,36,37,38], and little on the extreme multi-stability related to the initial conditions of non-memristors
We present a new 5-D twomemristor-based jerk (TMJ) system and emphatically study complex dynamical effects induced by the initial conditions of memristors and non-memristors therein
Summary
A nonlinear dynamical system can exhibit chaotic dynamics for specific system parameters and initial conditions [1,2]. Memristor-based chaotic circuits and systems have been broadly investigated, since memristor is a special nonlinear circuit component with memory effect and synaptic plasticity [19,28,29] This particular type of chaotic circuit and system is conductive to deriving coexisting infinitely many attractors. To implement the initial-condition-related extreme multi-stability, an effective and simple method is to introduce memristor into an existing dynamical system to construct a new memristor-based dynamical system, which is different from the method of using periodic trigonometric function to realize the initial condition-boosted infinitely many attractors in some special boostable systems [33,34]. We present a new 5-D TMJ system and emphatically study complex dynamical effects induced by the initial conditions of memristors and non-memristors therein.
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