Multiple Transient Transitions Behavior Analysis of a Double Memristor’s Hidden System and Its Circuit

Abstract

In this paper, a low-dimensional hidden nonlinear system is constructed by replacing two linear resistors of a simple integrating circuit with two active memristors. The system was analyzed in detail by using the Lyapunov exponent, 0-1 Test, Poincaré map, phase diagram, power spectral density diagram, timedomain waveform, and chaotic characteristic diagram. The results show that the system can oscillate by itself under zero initial conditions, and there are various transient transition behaviors, such as from chaos to limit cycle, chaos to quasi-periodic, quasi-periodic to another quasi-periodic transition, quasi-periodic to periodic transition. Besides, these transient processes themselves include 2, 3, 4, and 5 different states respectively, showing multiple transient transitions behavior, which are not reported in the related literature. It is also found that the initial states of these transition states have rich symmetrical attractors and the stable state is multistability. In addition, the global entropy analysis method is adopted to test the universal existence of transient behaviors, which demonstrates that the system has rich nonlinear characteristics. Finally, the memristive circuit verifies the system's physical feasibility and enriches the application of memristors in circuit theory. INDEX TERMS Active memristor, hidden attractor, multiple transient transitions, chaos, simple integrating circuit.

Complex dynamics analysis and feedback control for a memristive switched chaotic system

“…The multistability and transient characteristics in nonlinear systems have attracted much attention because of their complex and changeable states. Licai Liu proposed a 3-D double-memristor system, which reveals the existence of multi-transient behaviors for the first time [18]. At present, different types of transient behavior have been found in various memristor chaotic systems, which fully proves that memristors can indeed improve the complexity of the system [40][41][42][43][44][45].…”

“…For example, Lidan Wang et al proposed a mathematical model of a memristor and applied it to a third-order system, and confirmed the chaotic properties of the third-order system by circuit simulation [17]. By replacing linear resistors with two active memristors, Chuanhong Du constructed a nonlinear hidden system, which has multistable properties [18]. Han Bao et al proposed a new 5-D twomemristor-based jerk system and studied complex dynamical effects induced by memristor and non-memristor initial conditions therein [19].…”

Dynamical Analysis and Sampled-Data Stabilization of Memristor-Based Chua’s Circuits

“…By this action, the functional relationship between the flux and charge is given in (1) is realized. A detailed description of this memristor model is given [46], [47], [52]. A memristive Chua's oscillator circuit with a monotoneincreasing and piecewise linear memristor is presented in Fig.…”

A 5-D memristive hyperchaotic system with extreme multistability and its application in image encryption

“…This property has made chaos a crucial tool in information processing and randomness. Recently, within the realm of chaos system research, memristors have sparked significant interest among scholars [5][6][7]. Memristors possess nonlinear resistance characteristics, capable of storing charge and memorizing current direction, making them ideal components for constructing chaos systems.…”