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Stamov T, Stamov G, Stamova I, Gospodinova E. Lyapunov approach to manifolds stability for impulsive Cohen-Grossberg-type conformable neural network models. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:15431-15455. [PMID: 37679186 DOI: 10.3934/mbe.2023689] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/09/2023]
Abstract
In this paper, motivated by the advantages of the generalized conformable derivatives, an impulsive conformable Cohen-Grossberg-type neural network model is introduced. The impulses, which can be also considered as a control strategy, are at fixed instants of time. We define the notion of practical stability with respect to manifolds. A Lyapunov-based analysis is conducted, and new criteria are proposed. The case of bidirectional associative memory (BAM) network model is also investigated. Examples are given to demonstrate the effectiveness of the established results.
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Affiliation(s)
- Trayan Stamov
- Department of Engineering Design, Technical University of Sofia, Sofia 1000, Bulgaria
| | - Gani Stamov
- Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio TX 78249, USA
| | - Ivanka Stamova
- Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio TX 78249, USA
| | - Ekaterina Gospodinova
- Department of Computer Sciences, Technical University of Sofia, Sliven 8800, Bulgaria
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2
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Linkage-constraint Criteria for Robust Exponential Stability of Nonlinear BAM System with Derivative Contraction Coefficients and Piecewise Constant Arguments. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.08.078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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3
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Discrete Bidirectional Associative Memory Neural Networks of the Cohen–Grossberg Type for Engineering Design Symmetry Related Problems: Practical Stability of Sets Analysis. Symmetry (Basel) 2022. [DOI: 10.3390/sym14020216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make them very appropriate for different engineering design problems. However, the qualitative properties of the neural networks’ states are extremely important for their design and practical performance. In addition, the variety of neural network models requires the formulation of appropriate qualitative criteria. This paper studies a class of discrete Bidirectional Associative Memory (BAM) neural networks of the Cohen–Grossberg type that can be applied in engineering design. Due to the nature of the proposed models, they are very suitable for symmetry-related problems. The notion of the practical stability of the states with respect to sets is introduced. The practical stability analysis is conducted by the method of the Lyapunov functions. Examples are presented to verify the proposed criteria and demonstrate the efficiency of the results. Since engineering design is a constrained processes, the obtained stability of the sets’ results can be applied to numerous engineering design tasks of diverse interest.
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Chandrasekar A, Radhika T, Zhu Q. Further Results on Input-to-State Stability of Stochastic Cohen–Grossberg BAM Neural Networks with Probabilistic Time-Varying Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10649-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Othmani S, Tatar NE. Stability for a retarded impulsive Cohen–Grossberg BAM neural network system. J EXP THEOR ARTIF IN 2021. [DOI: 10.1080/0952813x.2021.1966840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Sakina Othmani
- Laboratory of SDG, Faculty of Mathematics University of Science and Technology Houari Boumedienne, Algiers, Algeria
| | - Nasser-eddine Tatar
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Interdisciplinary Research Center for Intelligent Manufacturing & Robotics, Dhahran, Saudi Arabia
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6
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Zhou Z, Liao H, Zhang Z. Global asymptotic stability for discrete-time Cohen-Grossberg neural networks with delays by combining graph theoretic approach with Homeomorphism concept. J EXP THEOR ARTIF IN 2020. [DOI: 10.1080/0952813x.2020.1801854] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Zheng Zhou
- School of Applied Mathematics, Xiamen University of Technology, Xiamen, China
| | - Huaying Liao
- Department of Mathematics and Computer Science, Nanchang Normal University, Nanchang, China
| | - Zhengqiu Zhang
- College of Mathematics and Econometrics, Hunan University, Changsha, China
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Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations. MATHEMATICS 2020. [DOI: 10.3390/math8071082] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincarѐ-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results.
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Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks. MATHEMATICS 2020. [DOI: 10.3390/math8050801] [Citation(s) in RCA: 40] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.
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On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays. MATHEMATICS 2020. [DOI: 10.3390/math8030335] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria.
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10
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Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10206-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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11
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Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms. MATHEMATICS 2019. [DOI: 10.3390/math8010027] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.
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Rao R, Zhong S, Pu Z. Fixed point and p-stability of T–S fuzzy impulsive reaction–diffusion dynamic neural networks with distributed delay via Laplacian semigroup. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.01.051] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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13
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Yu T, Wang H, Su M, Cao D. Distributed-delay-dependent exponential stability of impulsive neural networks with inertial term. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.06.033] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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14
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Global Exponential Synchronization of Complex-Valued Neural Networks with Time Delays via Matrix Measure Method. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9805-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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15
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Guan K, Wang Q. Impulsive Control for a Class of Cellular Neural Networks with Proportional Delay. Neural Process Lett 2018. [DOI: 10.1007/s11063-017-9776-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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16
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Zhou Y, Li C, Chen L, Huang T. Global exponential stability of memristive Cohen–Grossberg neural networks with mixed delays and impulse time window. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.11.011] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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17
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Chen WH, Luo S, Zheng WX. Generating Globally Stable Periodic Solutions of Delayed Neural Networks With Periodic Coefficients via Impulsive Control. IEEE TRANSACTIONS ON CYBERNETICS 2017; 47:1590-1603. [PMID: 30148709 DOI: 10.1109/tcyb.2016.2552383] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper is dedicated to designing periodic impulsive control strategy for generating globally stable periodic solutions for periodic neural networks with discrete and unbounded distributed delays when such neural networks do not have stable periodic solutions. Two criteria for the existence of globally exponentially stable periodic solutions are developed. The first one can deal with the case where no bounds on the derivative of the discrete delay are given, while the second one is a refined version of the first one when the discrete delay is constant. Both stability criteria possess several adjustable parameters, which will increase the flexibility for designing impulsive control laws. In particular, choosing appropriate adjustable parameters can lead to partial state impulsive control laws for certain periodic neural networks. The proof techniques employed includes two aspects. In the first aspect, by choosing a weighted phase space PCα, a sufficient condition for the existence of a unique periodic solution is derived by virtue of the contraction mapping principle. In the second aspect, by choosing an impulse-time-dependent Lyapunov function/functional to capture the dynamical characteristics of the impulsively controlled neural networks, improved stability criteria for periodic solutions are attained. Three numerical examples are given to illustrate the efficiency of the proposed results.
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19
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Zhang ZM, He Y, Zhang CK, Wu M. Exponential stabilization of neural networks with time-varying delay by periodically intermittent control. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.05.022] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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20
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Zhou Q, Wan L, Fu H, Zhang Q. Pullback attractor for Cohen–Grossberg neural networks with time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.06.069] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Muralisankar S, Manivannan A, Balasubramaniam P. Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks. ISA TRANSACTIONS 2015; 58:11-19. [PMID: 25862099 DOI: 10.1016/j.isatra.2015.03.004] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2013] [Revised: 10/15/2014] [Accepted: 03/14/2015] [Indexed: 06/04/2023]
Abstract
The aim of this manuscript is to investigate the mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks with time-delays. The time-delays are assumed to be interval time-varying and randomly occurring. Based on the new Lyapunov-Krasovskii functional and stochastic analysis approach, a novel sufficient condition is obtained in the form of linear matrix inequality such that the delayed stochastic neural networks are globally robustly asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, the derived theoretical results are validated through numerical examples in which maximum allowable upper bounds are calculated for different lower bounds of time-delay.
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Affiliation(s)
- S Muralisankar
- School of Mathematics, Madurai Kamaraj University, Madurai 625 021, Tamil Nadu, India.
| | - A Manivannan
- School of Mathematics, Madurai Kamaraj University, Madurai 625 021, Tamil Nadu, India.
| | - P Balasubramaniam
- Department of Mathematics, Gandhigram Rural Institute - Deemed University, Dindigul 624 302, Tamil Nadu, India.
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Niamsup P, Ratchagit K, Phat V. Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.02.030] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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24
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Robust stability of stochastic fuzzy delayed neural networks with impulsive time window. Neural Netw 2015; 67:84-91. [PMID: 25897509 DOI: 10.1016/j.neunet.2015.03.010] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2014] [Revised: 03/16/2015] [Accepted: 03/19/2015] [Indexed: 11/23/2022]
Abstract
The urgent problem of impulsive moments which cannot be determined in advance brings new challenges beyond the conventional impulsive systems theory. In order to solve this problem, the novel concept of impulsive time window is proposed in this paper. And the stability problem of stochastic fuzzy uncertain delayed neural networks with impulsive time window is investigated. By combining the discretized Lyapunov function approach with mathematical induction method, several novel and easy-to-check sufficient conditions concerning the impulsive time window are derived to ensure that the model considered here is exponentially stable in mean square. Numerical simulations are presented to further demonstrate the effectiveness of the proposed stability criterion.
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25
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Wei L, Chen WH. Global exponential stability of a class of impulsive neural networks with unstable continuous and discrete dynamics. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.06.072] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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26
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Şaylı M, Yılmaz E. Global robust asymptotic stability of variable-time impulsive BAM neural networks. Neural Netw 2014; 60:67-73. [DOI: 10.1016/j.neunet.2014.07.016] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2014] [Accepted: 07/31/2014] [Indexed: 10/24/2022]
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27
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Improved robust stability criteria for bidirectional associative memory neural networks under parameter uncertainties. Neural Comput Appl 2014. [DOI: 10.1007/s00521-014-1600-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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28
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Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park JH, Jung H. Effects of leakage time-varying delays in Markovian jump neural networks with impulse control. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2013.05.018] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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29
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New LMI-based conditions for global exponential stability to a class of Cohen–Grossberg BAM networks with delays. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2013.05.016] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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30
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Li X, Song S. Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2013; 24:868-877. [PMID: 24808469 DOI: 10.1109/tnnls.2012.2236352] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In this paper, a class of recurrent neural networks with discrete and continuously distributed delays is considered. Sufficient conditions for the existence, uniqueness, and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations. The proposed method, which differs from the existing results in the literature, shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent. Two numerical examples and their computer simulations are offered to show the effectiveness of our new results.
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31
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Stability analysis of reaction–diffusion Cohen–Grossberg neural networks under impulsive control. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2012.11.006] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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32
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Zhang Y. Robust exponential stability of uncertain impulsive neural networks with time-varying delays and delayed impulses. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2011.05.004] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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33
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Balasubramaniam P, Nagamani G. A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay. Neurocomputing 2011. [DOI: 10.1016/j.neucom.2011.01.011] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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34
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Tian A, Gai M, Shi B, Zhang Q. Existence and exponential stability of periodic solution for a class of Cohen–Grossberg-type BAM neural networks. Neurocomputing 2010. [DOI: 10.1016/j.neucom.2010.06.011] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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35
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Xiaodi Li, Jianhua Shen. LMI Approach for Stationary Oscillation of Interval Neural Networks With Discrete and Distributed Time-Varying Delays Under Impulsive Perturbations. ACTA ACUST UNITED AC 2010; 21:1555-63. [DOI: 10.1109/tnn.2010.2061865] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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36
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Global Passivity Analysis of Interval Neural Networks with Discrete and Distributed Delays of Neutral Type. Neural Process Lett 2010. [DOI: 10.1007/s11063-010-9147-8] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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37
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