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Ou S, Guo Z, Wen S, Huang T. Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules. Neural Netw 2024; 180:106713. [PMID: 39265482 DOI: 10.1016/j.neunet.2024.106713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2024] [Revised: 08/03/2024] [Accepted: 09/06/2024] [Indexed: 09/14/2024]
Abstract
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 3n 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 3n synchronization manifolds, wherein n 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.
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Affiliation(s)
- Shiqin Ou
- School of Mathematics and Statistics, Guizhou University, Guiyang 550025, 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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Zhou X, Cao J, Guan ZH, Wang X, Kong F. Fast synchronization control and application for encryption-decryption of coupled neural networks with intermittent random disturbance. Neural Netw 2024; 176:106404. [PMID: 38820802 DOI: 10.1016/j.neunet.2024.106404] [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: 01/01/2024] [Revised: 04/14/2024] [Accepted: 05/20/2024] [Indexed: 06/02/2024]
Abstract
In this paper, we design a new class of coupled neural networks with stochastically intermittent disturbances, in which the perturbation mechanism is different from other existed random neural networks. It is significant to construct the new models, which can simulate a class of the real neural networks in the disturbed environment, and the fast synchronization control strategies are studied by an adjustable parameter α. A controller with coupling signal is designed to study the exponential synchronization problem, meanwhile, another effective controller with not only adjustable synchronization rate but also with infinite gain avoided is used to investigate the preset-time synchronization. The fast synchronization conditions have been obtained by Lyapunov stability principle, Laplacian matrix and some inequality techniques. A numerical example shows the effectiveness of the control schemes, and the different control factors for synchronization rate are given to discuss the control effect. In particular, the image encryption-decryption based on drive-response networks has been successfully applied.
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Affiliation(s)
- Xianghui Zhou
- School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 211189, China; Ahlia University, Manama 10878, Bahrain
| | - Zhi-Hong Guan
- School of Artificial Intelligence and Automation. HUST, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xin Wang
- School of Computer Science and Technology, Huaiyin Normal University, Huaian 223300, Jiangsu, China
| | - Fanchao Kong
- School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China
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Zhang H, Zeng Z. Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:7555-7566. [PMID: 35100127 DOI: 10.1109/tnnls.2022.3144222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.
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Li K, Bai Y, Ma Z, Cao J. Feedback Pinning Control of Successive Lag Synchronization on a Dynamical Network. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:9490-9503. [PMID: 33705344 DOI: 10.1109/tcyb.2021.3061700] [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
In nature and human society, successive lag synchronization (SLS) is an important synchronization phenomenon. Compared with other synchronization patterns, the control theory of SLS is very lacking. To this end, we first introduce a complex dynamical network model with distributed delayed couplings, and design both the linear feedback pinning control and adaptive feedback pinning control to push SLS to the desired trajectories. Second, we obtain a series of sufficient conditions to achieve SLS to a desired trajectory with global stability. What is more, the control flow of SLS is given to show how to pick the pinned nodes accurately and set the feedback gains as well. Finally, since time-varying delay is common, we extend the constant time delay in SLS to be time varying. We find that the proposed pinning control schemes are still feasible if the coupling terms are appropriately adjusted. The theoretical results are verified on a neural network and the coupled Chua's circuits.
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Cao Y, Zhao L, Wen S, Huang T. Lag H∞ synchronization of coupled neural networks with multiple state couplings and multiple delayed state couplings. Neural Netw 2022; 151:143-155. [DOI: 10.1016/j.neunet.2022.03.032] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Revised: 02/07/2022] [Accepted: 03/28/2022] [Indexed: 11/29/2022]
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Zhuang J, Zhou Y, Xia Y. Intra-layer Synchronization in Duplex Networks with Time-Varying Delays and Stochastic Perturbations Under Impulsive Control. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10281-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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7
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Zhao LH, Wang JL. Lag H∞ synchronization and lag synchronization for multiple derivative coupled complex networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.11.100] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Yao W, Wang C, Cao J, Sun Y, Zhou C. Hybrid multisynchronization of coupled multistable memristive neural networks with time delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.07.014] [Citation(s) in RCA: 67] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Tang R, Yang X, Wan X. Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers. Neural Netw 2019; 113:79-90. [DOI: 10.1016/j.neunet.2018.11.010] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2018] [Revised: 10/24/2018] [Accepted: 11/14/2018] [Indexed: 10/27/2022]
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10
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Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.11.020] [Citation(s) in RCA: 100] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Lv X, Li X, Cao J, Perc M. Dynamical and Static Multisynchronization of Coupled Multistable Neural Networks via Impulsive Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:6062-6072. [PMID: 29993915 DOI: 10.1109/tnnls.2018.2816924] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper investigates the dynamical multisynchronization and static multisynchronization problem for delayed coupled multistable neural networks with fixed and switching topologies. To begin with, a class of activation functions as well as several sufficient conditions are introduced to ensure that every subnetwork has multiple equilibrium states. By constructing an appropriate Lyapunov function and by employing impulsive control theory and the average impulsive interval method, several sufficient conditions for multisynchronization in terms of linear matrix inequalities (LMIs) are obtained. Moreover, a unified impulsive controller is designed by means of the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness of the presented impulsive control strategy.
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Huang Z, Bin H, Cao J, Wang B. Synchronizing Neural Networks With Proportional Delays Based on a Class of -Type Allowable Time Scales. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:3418-3428. [PMID: 28796624 DOI: 10.1109/tnnls.2017.2729588] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Without confines of the continuous-time domain, this paper addresses synchronization control problem of neural networks in the face of multiple proportional delays on general time scales. The idea to deal with proportional delays is to propose a class of -type allowable time scales on which we design an appropriate controller to achieve exponential synchronization based on a calculus theory on time scales and Lyapunov function/functional methods. It is shown that adopting properties of -type time scales is an effective approach to establish synchronization for the networks with proportional delays. This helps us to have insight into the synchronization problems on general intermittent time domain. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.
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Fei Z, Guan C, Gao H, Fei Z, Guan C, Gao H. Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:2558-2567. [PMID: 28504952 DOI: 10.1109/tnnls.2017.2700321] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper is concerned with the exponential synchronization for master-slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( , , )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example.
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Li XJ, Yang GH. FLS-Based Adaptive Synchronization Control of Complex Dynamical Networks With Nonlinear Couplings and State-Dependent Uncertainties. IEEE TRANSACTIONS ON CYBERNETICS 2016; 46:171-180. [PMID: 25720020 DOI: 10.1109/tcyb.2015.2399334] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This paper is concerned with the problem of synchronization control of complex dynamical networks (CDN) subject to nonlinear couplings and uncertainties. An fuzzy logical system-based adaptive distributed controller is designed to achieve the synchronization. The asymptotic convergence of synchronization errors is analyzed by combining algebraic graph theory and Lyapunov theory. In contrast to the existing results, the proposed synchronization control method is applicable for the CDN with system uncertainties and unknown topology. Especially, the considered uncertainties are allowed to occur in the node local dynamics as well as in the interconnections of different nodes. In addition, it is shown that a unified controller design framework is derived for the CDN with or without coupling delays. Finally, simulations on a Chua's circuit network are provided to validate the effectiveness of the theoretical results.
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15
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Mean square exponential stability of stochastic fuzzy delayed Cohen–Grossberg neural networks with expectations in the coefficients. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.04.020] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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16
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Wang G, Shen Y, Yin Q. Synchronization Analysis of Coupled Stochastic Neural Networks with On–Off Coupling and Time-Delay. Neural Process Lett 2014. [DOI: 10.1007/s11063-014-9369-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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17
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Wu H, Zhang X, Li R, Yao R. Adaptive exponential synchronization of delayed Cohen–Grossberg neural networks with discontinuous activations. INT J MACH LEARN CYB 2014. [DOI: 10.1007/s13042-014-0258-9] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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18
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Design of a grey-prediction self-organizing fuzzy controller for active suspension systems. Appl Soft Comput 2013. [DOI: 10.1016/j.asoc.2013.06.003] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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19
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Exponential synchronization of coupled fuzzy neural networks with disturbances and mixed time-delays. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2012.10.018] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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20
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Wu ZG, Shi P, Su H, Chu J. Sampled-data synchronization of chaotic Lur'e systems with time delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2013; 24:410-421. [PMID: 24808314 DOI: 10.1109/tnnls.2012.2236356] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
This paper studies the problem of sampled-data control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems with time delays. It is assumed that the sampling periods are arbitrarily varying but bounded. In order to take full advantage of the available information about the actual sampling pattern, a novel Lyapunov functional is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Based on the Lyapunov functional, an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems. The desired sampled-data controller is designed by a linear matrix inequality approach. The effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of Chua's circuit and neural network.
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Gan Q. Exponential Synchronization of Stochastic Fuzzy Cellular Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control. Neural Process Lett 2012. [DOI: 10.1007/s11063-012-9254-9] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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22
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23
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Lian RJ. Intelligent control of a constant turning force system with fixed metal removal rate. Appl Soft Comput 2012. [DOI: 10.1016/j.asoc.2012.05.012] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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24
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Gan Q. Synchronization of unknown chaotic neural networks with stochastic perturbation and time delay in the leakage term based on adaptive control and parameter identification. Neural Comput Appl 2012. [DOI: 10.1007/s00521-012-0871-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Yu J, Yi Z, Zhou J. Continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons. IEEE TRANSACTIONS ON NEURAL NETWORKS 2010; 21:1690-1695. [PMID: 20813637 DOI: 10.1109/tnn.2010.2067224] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Continuous attractors of Lotka-Volterra recurrent neural networks (LV RNNs) with infinite neurons are studied in this brief. A continuous attractor is a collection of connected equilibria, and it has been recognized as a suitable model for describing the encoding of continuous stimuli in neural networks. The existence of the continuous attractors depends on many factors such as the connectivity and the external inputs of the network. A continuous attractor can be stable or unstable. It is shown in this brief that a LV RNN can possess multiple continuous attractors if the synaptic connections and the external inputs are Gussian-like in shape. Moreover, both stable and unstable continuous attractors can coexist in a network. Explicit expressions of the continuous attractors are calculated. Simulations are employed to illustrate the theory.
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Affiliation(s)
- Jiali Yu
- Institute for Infocomm Research, Agency for Science Technology and Research, 138632, Singapore.
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Donglian Qi, Meiqin Liu, Meikang Qiu, Senlin Zhang. Exponential ${\rm H}_{\infty}$ Synchronization of General Discrete-Time Chaotic Neural Networks With or Without Time Delays. ACTA ACUST UNITED AC 2010; 21:1358-65. [DOI: 10.1109/tnn.2010.2050904] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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28
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Li X. Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects. Neurocomputing 2010. [DOI: 10.1016/j.neucom.2009.10.016] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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29
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Existence and global attractivity of almost periodic solutions for delayed high-ordered neural networks. Neurocomputing 2010. [DOI: 10.1016/j.neucom.2009.10.007] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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