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Brahmi H, Ammar B, Ksibi A, Cherif F, Aldehim G, Alimi AM. Finite-time complete periodic synchronization of memristive neural networks with mixed delays. Sci Rep 2023; 13:12545. [PMID: 37532702 PMCID: PMC10397264 DOI: 10.1038/s41598-023-37737-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 06/27/2023] [Indexed: 08/04/2023] Open
Abstract
In this paper we study the oscillatory behavior of a new class of memristor based neural networks with mixed delays and we prove the existence and uniqueness of the periodic solution of the system based on the concept of Filippov solutions of the differential equation with discontinuous right-hand side. In addition, some assumptions are determined to guarantee the globally exponentially stability of the solution. Then, we study the adaptive finite-time complete periodic synchronization problem and by applying Lyapunov-Krasovskii functional approach, a new adaptive controller and adaptive update rule have been developed. A useful finite-time complete synchronization condition is established in terms of linear matrix inequalities. Finally, an illustrative simulation is given to substantiate the main results.
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Affiliation(s)
- Hajer Brahmi
- Research Groups on Intelligent Machines, National Engineering School of Sfax, University of Sfax, 3038, Sfax, Tunisia
| | - Boudour Ammar
- Research Groups on Intelligent Machines, National Engineering School of Sfax, University of Sfax, 3038, Sfax, Tunisia.
| | - Amel Ksibi
- Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
| | - Farouk Cherif
- Laboratory of Math Physics, Specials Functions and Applications LR11ES35, Department of Mathematics, ESSTHS, University of Sousse, Tunisia
| | - Ghadah Aldehim
- Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
| | - Adel M Alimi
- Research Groups on Intelligent Machines, National Engineering School of Sfax, University of Sfax, 3038, Sfax, Tunisia
- Department of Electrical and Electronic Engineering Science, Faculty of Engineering and the Built Environment, University of Johannesburg, South Africa
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Gan Q, Li L, Yang J, Qin Y, Meng M. Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5542-5556. [PMID: 33852405 DOI: 10.1109/tnnls.2021.3070966] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.
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Adaptive finite-time cluster synchronization of neutral-type coupled neural networks with mixed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.11.046] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Zheng CD, Xie F. Synchronization of delayed memristive neural networks by establishing novel Lyapunov functional. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.08.060] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Exponential Stability and Sampled-Data Synchronization of Delayed Complex-Valued Memristive Neural Networks. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10082-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order. MATHEMATICS 2019. [DOI: 10.3390/math7060559] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.
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The global exponential pseudo almost periodic synchronization of quaternion-valued cellular neural networks with time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.04.044] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Zheng CD, Zhang Y, Wang Z. Synchronization for memristive chaotic neural networks using Wirtinger-based multiple integral inequality. INT J MACH LEARN CYB 2018. [DOI: 10.1007/s13042-016-0626-8] [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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Wang D, Huang L, Tang L. Synchronization Criteria for Discontinuous Neural Networks With Mixed Delays via Functional Differential Inclusions. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:1809-1821. [PMID: 28422694 DOI: 10.1109/tnnls.2017.2688327] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper investigates the issue of global exponential synchronization for a class of general neural networks that contains discontinuous activation functions and mixed time delays. Functional differential inclusions and nonsmooth analysis theories are used as bases to design discontinuous controllers, such that the discontinuous neural networks can be exponential complete synchronized. This novel approach and its applicability to neural networks with continuous activations are also easily verified. Several numerical examples demonstrate the practicality and effectiveness of the design method.
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Zhang Z, Li A, Yang L. Global Asymptotic Periodic Synchronization for Delayed Complex-Valued BAM Neural Networks via Vector-Valued Inequality Techniques. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9722-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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12
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Synchronization Control of Coupled Memristor-Based Neural Networks with Mixed Delays and Stochastic Perturbations. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9675-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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13
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Stability Analysis for Memristive Recurrent Neural Network Under Different External Stimulus. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9671-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Zhang X, Niu P, Ma Y, Wei Y, Li G. Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition. Neural Netw 2017; 94:67-75. [PMID: 28753446 DOI: 10.1016/j.neunet.2017.06.010] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Revised: 06/01/2017] [Accepted: 06/22/2017] [Indexed: 11/28/2022]
Abstract
This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results.
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Affiliation(s)
- Xinxin Zhang
- School of Electrical Engineering, Yanshan University, Qinhuangdao 066001, China.
| | - Peifeng Niu
- School of Electrical Engineering, Yanshan University, Qinhuangdao 066001, China.
| | - Yunpeng Ma
- School of Electrical Engineering, Yanshan University, Qinhuangdao 066001, China
| | - Yanqiao Wei
- School of Electrical Engineering, Yanshan University, Qinhuangdao 066001, China
| | - Guoqiang Li
- School of Electrical Engineering, Yanshan University, Qinhuangdao 066001, China
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Feng J, Ma Q, Qin S. Exponential Stability of Periodic Solution for Impulsive Memristor-Based Cohen–Grossberg Neural Networks with Mixed Delays. INT J PATTERN RECOGN 2017. [DOI: 10.1142/s0218001417500227] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Memristor, as the future of artificial intelligence, has been widely used in pattern recognition or signal processing from sensor arrays. Memristor-based recurrent neural network (MRNN) is an ideal model to mimic the functionalities of the human brain due to the physical properties of memristor. In this paper, the periodicity for memristor-based Cohen–Grossberg neural networks (MCGNNs) is studied. The neural network (NN) considered in this paper is based on the memristor and involves time-varying delays, distributed delays and impulsive effects. The boundedness and monotonicity of the activation function are not assumed. By some inequality technique and contraction mapping principle, we prove the existence, uniqueness and exponential stability of periodic solution for MCGNNs. Finally, some numeral examples and comparisons are provided to illustrate the validation of our results.
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Affiliation(s)
- Jiqiang Feng
- Institute of Intelligent Computing Science, Shenzhen University, Shenzhen 518060, P. R. China
| | - Qiang Ma
- Department of Mathematics, Harbin Institute of Technology, Weihai 264209, P. R. China
| | - Sitian Qin
- Department of Mathematics, Harbin Institute of Technology, Weihai 264209, P. R. China
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Wu H, Wang L, Niu P, Wang Y. Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.01.022] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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17
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Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control. INT J MACH LEARN CYB 2017. [DOI: 10.1007/s13042-017-0646-z] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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18
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Zheng CD, Xian Y. On synchronization for chaotic memristor-based neural networks with time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.08.028] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Wang Z, Ding S, Huang Z, Zhang H. Exponential Stability and Stabilization of Delayed Memristive Neural Networks Based on Quadratic Convex Combination Method. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2016; 27:2337-2350. [PMID: 26513808 DOI: 10.1109/tnnls.2015.2485259] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.
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Novel Switching Jumps Dependent Exponential Synchronization Criteria for Memristor-Based Neural Networks. Neural Process Lett 2016. [DOI: 10.1007/s11063-016-9504-3] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Periodic synchronization control of discontinuous delayed networks by using extended Filippov-framework. Neural Netw 2015; 68:96-110. [DOI: 10.1016/j.neunet.2015.04.011] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2015] [Revised: 04/09/2015] [Accepted: 04/27/2015] [Indexed: 11/24/2022]
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22
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Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.03.069] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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