{"title":"具有状态相关切换规则的切换神经网络的多稳定性和固定时间多同步性","authors":"","doi":"10.1016/j.neunet.2024.106713","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of <span><math><msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span> exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are <span><math><msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span> synchronization manifolds, wherein <span><math><mi>n</mi></math></span> is the number of neurons. Additionally, an estimation for the settling time required for drive–response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.</p></div>","PeriodicalId":49763,"journal":{"name":"Neural Networks","volume":null,"pages":null},"PeriodicalIF":6.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules\",\"authors\":\"\",\"doi\":\"10.1016/j.neunet.2024.106713\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of <span><math><msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span> exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are <span><math><msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span> synchronization manifolds, wherein <span><math><mi>n</mi></math></span> is the number of neurons. Additionally, an estimation for the settling time required for drive–response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.</p></div>\",\"PeriodicalId\":49763,\"journal\":{\"name\":\"Neural Networks\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.0000,\"publicationDate\":\"2024-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Neural Networks\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893608024006373\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neural Networks","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893608024006373","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了具有多个几乎周期解和与状态相关的切换规则的切换神经网络的多稳定性和固定时间同步的理论结果。本文表明,可以利用状态空间分区来表征开关神经网络几乎周期解的数量、位置和稳定性。本文导出了两组充分条件,以确定 3n 个指数稳定的近周期解的存在。随后,本文首次提出了开关神经网络中固定时间多同步的新概念,即在多个稳定均衡状态内与一系列近周期参数相关联。根据多稳态性结果,证明存在 3n 个同步流形,其中 n 为神经元数量。此外,本文还估算了驱动响应切换神经网络实现同步所需的沉淀时间。需要注意的是,本文将稳定平衡点(静态多同步)、稳定的近周期轨道(动态多同步)和混合稳定平衡状态(混合多同步)视为多稳态性(多同步)的特例。为证实理论结果,阐述了两个数值实例。
Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules
This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are synchronization manifolds, wherein is the number of neurons. Additionally, an estimation for the settling time required for drive–response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.
期刊介绍:
Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.