A symmetric oscillator with multi-stability and chaotic dynamics: bifurcations, circuit implementation, and impulsive control

Wang, Zhen; Veeman, Dhinakaran; Zhang, Min; Natiq, Hayder; Yang, Rui; Hussain, Iqtadar

doi:10.1140/epjs/s11734-021-00371-y

Cited by 6 publications

(1 citation statement)

References 52 publications

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“…Similar to a resistor, a capacitor, and an inductor, a memristor is defined as a nonvolatile nonlinear circuit element [1]. At the moment, memristor research is mostly focused on physical device preparation, characteristic analysis, and application research [2][3][4][5][6]. Furthermore, because of the limitations of its manufacturing method, the memristor has not been extensively industrialized.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors

Tian,

Zhao,

Liu

et al. 2024

Fractal Fract

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In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system’s attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation.

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