{"title":"一类广义记忆图中的混沌动力学。","authors":"Iram Hussan, Manyu Zhao, Xu Zhang","doi":"10.1063/5.0237251","DOIUrl":null,"url":null,"abstract":"<p><p>The memory effects of the memristors in nonlinear systems make the systems generate complicated dynamics, which inspires the development of the applications of memristors. In this article, the model of the discrete memristive systems with the generalized Ohm's law is introduced, where the classical Ohm's law is a linear relationship between voltage and current, and a generalized Ohm's law is a nonlinear relationship. To illustrate the rich dynamics of this model, the complicated dynamical behavior of three types of maps with three types of discrete memristances is investigated, where a cubic function representing a kind of generalized Ohm's law is used, and this cubic function is a simplified characteristic of the famous tunnel diode. The existence of attractors with one or two positive Lyapunov exponents (corresponding to chaotic or hyperchaotic dynamics) is obtained, and the coexistence of (infinitely) many attractors is observable. A hardware device is constructed to implement these maps and the analog voltage signals are experimentally acquired.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chaotic dynamics in a class of generalized memristive maps.\",\"authors\":\"Iram Hussan, Manyu Zhao, Xu Zhang\",\"doi\":\"10.1063/5.0237251\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The memory effects of the memristors in nonlinear systems make the systems generate complicated dynamics, which inspires the development of the applications of memristors. In this article, the model of the discrete memristive systems with the generalized Ohm's law is introduced, where the classical Ohm's law is a linear relationship between voltage and current, and a generalized Ohm's law is a nonlinear relationship. To illustrate the rich dynamics of this model, the complicated dynamical behavior of three types of maps with three types of discrete memristances is investigated, where a cubic function representing a kind of generalized Ohm's law is used, and this cubic function is a simplified characteristic of the famous tunnel diode. The existence of attractors with one or two positive Lyapunov exponents (corresponding to chaotic or hyperchaotic dynamics) is obtained, and the coexistence of (infinitely) many attractors is observable. A hardware device is constructed to implement these maps and the analog voltage signals are experimentally acquired.</p>\",\"PeriodicalId\":9974,\"journal\":{\"name\":\"Chaos\",\"volume\":\"34 11\",\"pages\":\"\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0237251\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0237251","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Chaotic dynamics in a class of generalized memristive maps.
The memory effects of the memristors in nonlinear systems make the systems generate complicated dynamics, which inspires the development of the applications of memristors. In this article, the model of the discrete memristive systems with the generalized Ohm's law is introduced, where the classical Ohm's law is a linear relationship between voltage and current, and a generalized Ohm's law is a nonlinear relationship. To illustrate the rich dynamics of this model, the complicated dynamical behavior of three types of maps with three types of discrete memristances is investigated, where a cubic function representing a kind of generalized Ohm's law is used, and this cubic function is a simplified characteristic of the famous tunnel diode. The existence of attractors with one or two positive Lyapunov exponents (corresponding to chaotic or hyperchaotic dynamics) is obtained, and the coexistence of (infinitely) many attractors is observable. A hardware device is constructed to implement these maps and the analog voltage signals are experimentally acquired.
期刊介绍:
Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.