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Zhou J, Ma X, Yan Z, Arik S. Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design. Neural Netw 2024; 169:733-743. [PMID: 37979499 DOI: 10.1016/j.neunet.2023.11.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Revised: 10/04/2023] [Accepted: 11/05/2023] [Indexed: 11/20/2023]
Abstract
This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L2-gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L2-gain analysis is established through the application of the Gronwall-Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov-Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach.
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Affiliation(s)
- Jianping Zhou
- School of Computer Science & Technology, Anhui University of Technology, Ma'anshan, 243032, Anhui, China
| | - Xiaofeng Ma
- School of Computer Science & Technology, Anhui University of Technology, Ma'anshan, 243032, Anhui, China
| | - Zhilian Yan
- School of Electrical & Information Engineering, Anhui University of Technology, Ma'anshan, 243032, Anhui, China
| | - Sabri Arik
- Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, 34320, Turkey.
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2
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He S, Vignesh D, Rondoni L, Banerjee S. Chaos and multi-layer attractors in asymmetric neural networks coupled with discrete fractional memristor. Neural Netw 2023; 167:572-587. [PMID: 37708779 DOI: 10.1016/j.neunet.2023.08.041] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Revised: 07/19/2023] [Accepted: 08/23/2023] [Indexed: 09/16/2023]
Abstract
This article introduces a novel model of asymmetric neural networks combined with fractional difference memristors, which has both theoretical and practical implications in the rapidly evolving field of computational intelligence. The proposed model includes two types of fractional difference memristor elements: one with hyperbolic tangent memductance and the other with periodic memductance and memristor state described by sine functions. The authenticity of the constructed memristor is confirmed through fingerprint verification. The research extensively investigates the dynamics of a coupled neural network model, analyzing its stability at equilibrium states, studying bifurcation diagrams, and calculating the largest Lyapunov exponents. The results suggest that when incorporating sine memristors, the model demonstrates coexisting state variables depending on the initial conditions, revealing the emergence of multi-layer attractors. The article further demonstrates how the memristor state shifts through numerical simulations with varying memductance values. Notably, the study emphasizes the crucial role of memductance (synaptic weight) in determining the complex dynamical characteristics of neural network systems. To support the analytical results and demonstrate the chaotic response of state variables, the article includes appropriate numerical simulations. These simulations effectively validate the presented findings and provide concrete evidence of the system's chaotic behavior.
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Affiliation(s)
- Shaobo He
- School of Automation and Electronic Information, Xiangtan University, Xiangtan, 411105, China.
| | - D Vignesh
- Department of Mathematics, School of Engineering and Technology, CMR University, Chagalahatti, Bangalore, 562149, Karnataka, India.
| | - Lamberto Rondoni
- Department of Mathematical Sciences, Giuseppe Luigi Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, Italy.
| | - Santo Banerjee
- Department of Mathematical Sciences, Giuseppe Luigi Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, Italy.
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3
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Long H, Ci J, Guo Z, Wen S, Huang T. Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances. Neural Netw 2023; 166:459-470. [PMID: 37574620 DOI: 10.1016/j.neunet.2023.07.045] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 05/29/2023] [Accepted: 07/27/2023] [Indexed: 08/15/2023]
Abstract
In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Han Long
- College of Science, National University of Defense Technology, Changsha 410073, China.
| | - Jingxuan Ci
- School of Mathematics, Hunan University, Changsha 410082, China.
| | - Zhenyuan Guo
- School of Mathematics, Hunan University, Changsha 410082, China.
| | - Shiping Wen
- Centre for Artificial Intelligence, Faculty of Engineering Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia.
| | - Tingwen Huang
- Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar.
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4
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Wu Z, Nie X, Cao B. Coexistence and local stability of multiple equilibrium points for fractional-order state-dependent switched competitive neural networks with time-varying delays. Neural Netw 2023; 160:132-147. [PMID: 36640489 DOI: 10.1016/j.neunet.2022.12.013] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Revised: 11/09/2022] [Accepted: 12/16/2022] [Indexed: 01/05/2023]
Abstract
This paper investigates the coexistence and local stability of multiple equilibrium points for a class of competitive neural networks with sigmoidal activation functions and time-varying delays, in which fractional-order derivative and state-dependent switching are involved at the same time. Some novel criteria are established to ensure that such n-neuron neural networks can have [Formula: see text] total equilibrium points and [Formula: see text] locally stable equilibrium points with m1+m2=n, based on the fixed-point theorem, the definition of equilibrium point in the sense of Filippov, the theory of fractional-order differential equation and Lyapunov function method. The investigation implies that the competitive neural networks with switching can possess greater storage capacity than the ones without switching. Moreover, the obtained results include the multistability results of both fractional-order switched Hopfield neural networks and integer-order switched Hopfield neural networks as special cases, thus generalizing and improving some existing works. Finally, four numerical examples are presented to substantiate the effectiveness of the theoretical analysis.
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Affiliation(s)
- Zhongwen Wu
- School of Mathematics, Southeast University, Nanjing, 211189, China.
| | - Xiaobing Nie
- School of Mathematics, Southeast University, Nanjing, 211189, China.
| | - Boqiang Cao
- School of Mathematics, Southeast University, Nanjing, 211189, China.
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5
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Liu P, Wang J, Zeng Z. An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:1098-1111. [PMID: 34449396 DOI: 10.1109/tnnls.2021.3105519] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The stability analysis of recurrent neural networks (RNNs) with multiple equilibria has received extensive interest since it is a prerequisite for successful applications of RNNs. With the increasing theoretical results on this topic, it is desirable to review the results for a systematical understanding of the state of the art. This article provides an overview of the stability results of RNNs with multiple equilibria including complete stability and multistability. First, preliminaries on the complete stability and multistability analysis of RNNs are introduced. Second, the complete stability results of RNNs are summarized. Third, the multistability results of various RNNs are reviewed in detail. Finally, future directions in these interesting topics are suggested.
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6
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Multiple asymptotical ω-periodicity of fractional-order delayed neural networks under state-dependent switching. Neural Netw 2023; 157:11-25. [DOI: 10.1016/j.neunet.2022.09.034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2021] [Revised: 09/28/2022] [Accepted: 09/29/2022] [Indexed: 11/06/2022]
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7
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Wan L, Liu Z. Multiple exponential stability and instability for state-dependent switched neural networks with time-varying delays and piecewise-linear radial basis activation functions. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.12.040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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8
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Guo Z, Ou S, Wang J. Multistability of Switched Neural Networks With Gaussian Activation Functions Under State-Dependent Switching. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:6569-6583. [PMID: 34077372 DOI: 10.1109/tnnls.2021.3082560] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article presents theoretical results on the multistability of switched neural networks with Gaussian activation functions under state-dependent switching. It is shown herein that the number and location of the equilibrium points of the switched neural networks can be characterized by making use of the geometrical properties of Gaussian functions and local linearization based on the Brouwer fixed-point theorem. Four sets of sufficient conditions are derived to ascertain the existence of 7p15p23p3 equilibrium points, and 4p13p22p3 of them are locally stable, wherein p1 , p2 , and p3 are nonnegative integers satisfying 0 ≤ p1+p2+p3 ≤ n and n is the number of neurons. It implies that there exist up to 7n equilibria, and up to 4n of them are locally stable when p1=n . It also implies that properly selecting p1 , p2 , and p3 can engender a desirable number of stable equilibria. Two numerical examples are elaborated to substantiate the theoretical results.
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9
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Multistability analysis of switched fractional-order recurrent neural networks with time-varying delay. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07592-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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10
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Yang J, Chen G, Wen S. Finite-time dissipative control for bidirectional associative memory neural networks with state-dependent switching and time-varying delays. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.109338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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11
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Multistability analysis of delayed recurrent neural networks with a class of piecewise nonlinear activation functions. Neural Netw 2022; 152:80-89. [DOI: 10.1016/j.neunet.2022.04.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Revised: 04/11/2022] [Accepted: 04/14/2022] [Indexed: 11/15/2022]
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12
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Xiao H, Zhu Q, Karimi HR. Stability of stochastic delay switched neural networks with all unstable subsystems: A multiple discretized Lyapunov-Krasovskii functionals method. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2021.09.027] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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13
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Peng L, Li X, Bi D, Xie X, Xie Y. Pinning multisynchronization of delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. Neural Netw 2021; 144:372-383. [PMID: 34555664 DOI: 10.1016/j.neunet.2021.08.029] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2021] [Revised: 07/13/2021] [Accepted: 08/26/2021] [Indexed: 11/19/2022]
Abstract
This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the N coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.
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Affiliation(s)
- Libiao Peng
- School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China.
| | - Xifeng Li
- School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China
| | - Dongjie Bi
- School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China
| | - Xuan Xie
- School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China
| | - Yongle Xie
- School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China.
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14
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Multistability of Hopfield neural networks with a designed discontinuous sawtooth-type activation function. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.05.045] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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15
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Nie X, Liu P, Liang J, Cao J. Exact coexistence and locally asymptotic stability of multiple equilibria for fractional-order delayed Hopfield neural networks with Gaussian activation function. Neural Netw 2021; 142:690-700. [PMID: 34403909 DOI: 10.1016/j.neunet.2021.07.029] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 06/08/2021] [Accepted: 07/26/2021] [Indexed: 11/30/2022]
Abstract
This paper explores the multistability issue for fractional-order Hopfield neural networks with Gaussian activation function and multiple time delays. First, several sufficient criteria are presented for ensuring the exact coexistence of 3n equilibria, based on the geometric characteristics of Gaussian function, the fixed point theorem and the contraction mapping principle. Then, different from the existing methods used in the multistability analysis of fractional-order neural networks without time delays, it is shown that 2n of 3n total equilibria are locally asymptotically stable, by applying the theory of fractional-order linear delayed system and constructing suitable Lyapunov function. The obtained results improve and extend some existing multistability works for classical integer-order neural networks and fractional-order neural networks without time delays. Finally, an illustrative example with comprehensive computer simulations is given to demonstrate the theoretical results.
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Affiliation(s)
- Xiaobing Nie
- The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing 211189, China.
| | - Pingping Liu
- The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing 211189, China
| | - Jinling Liang
- The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing 211189, China
| | - Jinde Cao
- The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing 211189, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
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16
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Shen Y, Zhu S, Liu X, Wen S. Multistability and associative memory of neural networks with Morita-like activation functions. Neural Netw 2021; 142:162-170. [PMID: 34000563 DOI: 10.1016/j.neunet.2021.04.035] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2020] [Revised: 04/11/2021] [Accepted: 04/26/2021] [Indexed: 11/25/2022]
Abstract
This paper presents the multistability analysis and associative memory of neural networks (NNs) with Morita-like activation functions. In order to seek larger memory capacity, this paper proposes Morita-like activation functions. In a weakened condition, this paper shows that the NNs with n-neurons have (2m+1)n equilibrium points (Eps) and (m+1)n of them are locally exponentially stable, where the parameter m depends on the Morita-like activation functions, called Morita parameter. Also the attraction basins are estimated based on the state space partition. Moreover, this paper applies these NNs into associative memories (AMs). Compared with the previous related works, the number of Eps and AM's memory capacity are extensively increased. The simulation results are illustrated and some reliable associative memories examples are shown at the end of this paper.
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Affiliation(s)
- Yuanchu Shen
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Song Zhu
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Xiaoyang Liu
- School of Computer Science and Technology, Jiangsu Normal University, Xuzhou, 221116, China.
| | - Shiping Wen
- Centre for Artificial Intelligence, University of Technology Sydney, Ultimo, NSW 2007, Australia.
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17
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Zhang J, Zhu S, Lu N, Wen S. Multistability of state-dependent switching neural networks with discontinuous nonmonotonic piecewise linear activation functions. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.01.046] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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18
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Multi-periodicity of switched neural networks with time delays and periodic external inputs under stochastic disturbances. Neural Netw 2021; 141:107-119. [PMID: 33887601 DOI: 10.1016/j.neunet.2021.03.039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2020] [Revised: 03/11/2021] [Accepted: 03/29/2021] [Indexed: 11/21/2022]
Abstract
This paper presents new theoretical results on the multi-periodicity of recurrent neural networks with time delays evoked by periodic inputs under stochastic disturbances and state-dependent switching. Based on the geometric properties of activation function and switching threshold, the neuronal state space is partitioned into 5n regions in which 3n ones are shown to be positively invariant with probability one. Furthermore, by using Itô's formula, Lyapunov functional method, and the contraction mapping theorem, two criteria are proposed to ascertain the existence and mean-square exponential stability of a periodic orbit in every positive invariant set. As a result, the number of mean-square exponentially stable periodic orbits increases to 3n from 2n in a neural network without switching. Two illustrative examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.
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19
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Long C, Zhang G, Zeng Z, Hu J. Finite-time lag synchronization of inertial neural networks with mixed infinite time-varying delays and state-dependent switching. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.059] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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20
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Liu P, Wang J, Guo Z. Multiple and Complete Stability of Recurrent Neural Networks With Sinusoidal Activation Function. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:229-240. [PMID: 32203032 DOI: 10.1109/tnnls.2020.2978267] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.
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