{"title":"Dynamics analysis and predefined-time sliding mode synchronization of multi-scroll systems based on a single memristor model","authors":"Shaohui Yan, Xinyu Wu, Jiawei Jiang","doi":"10.1016/j.chaos.2025.116337","DOIUrl":null,"url":null,"abstract":"<div><div>To overcome the limitations of conventional designs for memristive multi-scroll chaotic systems, this paper introduces a novel memristor that relies solely on a single memristor function and a single state variable function to generate both odd and even numbers of double-scroll attractors. This design not only simplifies the memristor structure but also offers a new approach to constructing multi-scroll chaotic systems. The proposed memristor is integrate into a modified Sprott-C system to develop the one-dimensional memristive multi-scroll Sprott-C systems (1D-MMSCS), two-dimensional memristive multi-scroll Sprott-C systems (2D-MMSCS), and the three-dimensional memristive multi-scroll Sprott-C systems (3D-MMSCS). The complex dynamics of these memristive multi-scroll systems are analyzed using equilibrium points, Poincaré maps, bifurcation diagrams, and Lyapunov exponents. Interestingly, the constructed MMSCS exhibits extreme multi-stability, indicating its high sensitivity to initial conditions and enhanced unpredictability. To verify the practical feasibility of the system, it is developed a digital hardware platform based on a Field-Programmable Gate Array (FPGA) and successfully implemented both the 1D-MMSCS and 2D-MMSCS. Finally, leveraging Lyapunov stability theory and predefined-time stability theory, a novel predefined-time sliding mode control scheme (PTSMS) is proposed. This scheme is applied to achieve synchronization in the more complex 3D-MMSCS. Simulation results confirm that the proposed method ensures rapid synchronization and exhibits strong robustness against internal uncertainties and external disturbances.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116337"},"PeriodicalIF":5.3000,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077925003509","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
To overcome the limitations of conventional designs for memristive multi-scroll chaotic systems, this paper introduces a novel memristor that relies solely on a single memristor function and a single state variable function to generate both odd and even numbers of double-scroll attractors. This design not only simplifies the memristor structure but also offers a new approach to constructing multi-scroll chaotic systems. The proposed memristor is integrate into a modified Sprott-C system to develop the one-dimensional memristive multi-scroll Sprott-C systems (1D-MMSCS), two-dimensional memristive multi-scroll Sprott-C systems (2D-MMSCS), and the three-dimensional memristive multi-scroll Sprott-C systems (3D-MMSCS). The complex dynamics of these memristive multi-scroll systems are analyzed using equilibrium points, Poincaré maps, bifurcation diagrams, and Lyapunov exponents. Interestingly, the constructed MMSCS exhibits extreme multi-stability, indicating its high sensitivity to initial conditions and enhanced unpredictability. To verify the practical feasibility of the system, it is developed a digital hardware platform based on a Field-Programmable Gate Array (FPGA) and successfully implemented both the 1D-MMSCS and 2D-MMSCS. Finally, leveraging Lyapunov stability theory and predefined-time stability theory, a novel predefined-time sliding mode control scheme (PTSMS) is proposed. This scheme is applied to achieve synchronization in the more complex 3D-MMSCS. Simulation results confirm that the proposed method ensures rapid synchronization and exhibits strong robustness against internal uncertainties and external disturbances.
期刊介绍:
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.