{"title":"多参数可控忆阻保守多波混沌系统的分析、实现及有限时间同步","authors":"Yizhe Li, Mu Li","doi":"10.1140/epjp/s13360-025-06290-4","DOIUrl":null,"url":null,"abstract":"<div><p>A three-dimensional memristive conservative multi-wave chaotic system is proposed, with low dimensionality, a simple mathematical model, and rich dynamical behaviors. The attractors with the three system parameters (<i>c</i>, <i>d</i>, <i>e</i>) will all show multi-wave changes, and with the parameter <i>e</i> changes in the multi-wave attractors can be symmetric state, in which we use the parameter <i>e</i> to explore the attractor formation mechanism, from the <i>x</i>–<i>z</i> plane, with the parameter <i>e</i> increases the attractor gradually stacked, and ultimately the formation of the attractor. In addition, with the change of the parameters <i>a</i> and <i>b</i>, the shape of the attractors will be changed, and when <i>a</i> and <i>b</i> are varied simultaneously, the maximum Lyapunov exponent of the system can reach 2.84. The chaotic, hidden and under certain conditions conservative features of the system are proved by analyzing the Lyapunov exponent, the Kaplan-Yorke dimension, and the equilibrium point. Furthermore, we discover that the system shows multiple coexisting attractors behavior, two kinds of offset-boosting behaviors, and three kinds of transient transfer behaviors. The system is then used for finite-time synchronization, which provides a reference for applications in real engineering. Finally, the system’s hardware is implemented using FPGA.</p></div>","PeriodicalId":792,"journal":{"name":"The European Physical Journal Plus","volume":"140 4","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis, implementation and finite-time synchronization of a multi-parameter controllable memristive conservative multi-wave chaotic system\",\"authors\":\"Yizhe Li, Mu Li\",\"doi\":\"10.1140/epjp/s13360-025-06290-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A three-dimensional memristive conservative multi-wave chaotic system is proposed, with low dimensionality, a simple mathematical model, and rich dynamical behaviors. The attractors with the three system parameters (<i>c</i>, <i>d</i>, <i>e</i>) will all show multi-wave changes, and with the parameter <i>e</i> changes in the multi-wave attractors can be symmetric state, in which we use the parameter <i>e</i> to explore the attractor formation mechanism, from the <i>x</i>–<i>z</i> plane, with the parameter <i>e</i> increases the attractor gradually stacked, and ultimately the formation of the attractor. In addition, with the change of the parameters <i>a</i> and <i>b</i>, the shape of the attractors will be changed, and when <i>a</i> and <i>b</i> are varied simultaneously, the maximum Lyapunov exponent of the system can reach 2.84. The chaotic, hidden and under certain conditions conservative features of the system are proved by analyzing the Lyapunov exponent, the Kaplan-Yorke dimension, and the equilibrium point. Furthermore, we discover that the system shows multiple coexisting attractors behavior, two kinds of offset-boosting behaviors, and three kinds of transient transfer behaviors. The system is then used for finite-time synchronization, which provides a reference for applications in real engineering. Finally, the system’s hardware is implemented using FPGA.</p></div>\",\"PeriodicalId\":792,\"journal\":{\"name\":\"The European Physical Journal Plus\",\"volume\":\"140 4\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2025-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The European Physical Journal Plus\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjp/s13360-025-06290-4\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal Plus","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjp/s13360-025-06290-4","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Analysis, implementation and finite-time synchronization of a multi-parameter controllable memristive conservative multi-wave chaotic system
A three-dimensional memristive conservative multi-wave chaotic system is proposed, with low dimensionality, a simple mathematical model, and rich dynamical behaviors. The attractors with the three system parameters (c, d, e) will all show multi-wave changes, and with the parameter e changes in the multi-wave attractors can be symmetric state, in which we use the parameter e to explore the attractor formation mechanism, from the x–z plane, with the parameter e increases the attractor gradually stacked, and ultimately the formation of the attractor. In addition, with the change of the parameters a and b, the shape of the attractors will be changed, and when a and b are varied simultaneously, the maximum Lyapunov exponent of the system can reach 2.84. The chaotic, hidden and under certain conditions conservative features of the system are proved by analyzing the Lyapunov exponent, the Kaplan-Yorke dimension, and the equilibrium point. Furthermore, we discover that the system shows multiple coexisting attractors behavior, two kinds of offset-boosting behaviors, and three kinds of transient transfer behaviors. The system is then used for finite-time synchronization, which provides a reference for applications in real engineering. Finally, the system’s hardware is implemented using FPGA.
期刊介绍:
The aims of this peer-reviewed online journal are to distribute and archive all relevant material required to document, assess, validate and reconstruct in detail the body of knowledge in the physical and related sciences.
The scope of EPJ Plus encompasses a broad landscape of fields and disciplines in the physical and related sciences - such as covered by the topical EPJ journals and with the explicit addition of geophysics, astrophysics, general relativity and cosmology, mathematical and quantum physics, classical and fluid mechanics, accelerator and medical physics, as well as physics techniques applied to any other topics, including energy, environment and cultural heritage.