1
|
Sheng Y, Zeng Z, Huang T. Finite-Time Stabilization of Competitive Neural Networks With Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:11325-11334. [PMID: 34133310 DOI: 10.1109/tcyb.2021.3082153] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article investigates finite-time stabilization of competitive neural networks with discrete time-varying delays (DCNNs). By virtue of comparison strategies and inequality techniques, finite-time stabilization of the underlying DCNNs is analyzed by designing a discontinuous state feedback controller, which simplifies the controller design and proof processes of some existing results. Meanwhile, global exponential stabilization of the DCNNs is provided under a continuous state feedback controller. In addition, global exponential stability of the DCNNs is shown as an M-matrix, which contains some published outcomes as special cases. Finally, three examples are given to illuminate the validity of the theories.
Collapse
|
2
|
Global Asymptotic Stability of Competitive Neural Networks with Reaction-Diffusion Terms and Mixed Delays. Symmetry (Basel) 2022. [DOI: 10.3390/sym14112224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
In this article, a new competitive neural network (CNN) with reaction-diffusion terms and mixed delays is proposed. Because this network system contains reaction-diffusion terms, it belongs to a partial differential system, which is different from the existing classic CNNs. First, taking into account the spatial diffusion effect, we introduce spatial diffusion for CNNs. Furthermore, since the time delay has an essential influence on the properties of the system, we introduce mixed delays including time-varying discrete delays and distributed delays for CNNs. By constructing suitable Lyapunov–Krasovskii functionals and virtue of the theories of delayed partial differential equations, we study the global asymptotic stability for the considered system. The effectiveness and correctness of the proposed CNN model with reaction-diffusion terms and mixed delays are verified by an example. Finally, some discussion and conclusions for recent developments of CNNs are given.
Collapse
|
3
|
Wang L, Zhang CK. Exponential Synchronization of Memristor-Based Competitive Neural Networks With Reaction-Diffusions and Infinite Distributed Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; PP:745-758. [PMID: 35622804 DOI: 10.1109/tnnls.2022.3176887] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Taking into account the infinite distributed delays and reaction-diffusions, this article investigates the global exponential synchronization problem of a class of memristor-based competitive neural networks (MCNNs) with different time scales. Based on the Lyapunov-Krasovskii functional and inequality approach, an adaptive control approach is proposed to ensure the exponential synchronization of the addressed drive-response networks. The closed-loop system is a discontinuous and delayed partial differential system in a cascade form, involving the spatial diffusion, the infinite distributed delays, the parametric adaptive law, the state-dependent switching parameters, and the variable structure controllers. By combining the theories of nonsmooth analysis, partial differential equation (PDE) and adaptive control, we present a new analytical method for rigorously deriving the synchronization of the states of the complex system. The derived m-norm (m ≥ 2)-based synchronization criteria are easily verified and the theoretical results are easily extended to memristor-based neural networks (NNs) without different time scales and reaction-diffusions. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results.
Collapse
|
4
|
Kurikawa T, Kaneko K. Multiple-Timescale Neural Networks: Generation of History-Dependent Sequences and Inference Through Autonomous Bifurcations. Front Comput Neurosci 2021; 15:743537. [PMID: 34955798 PMCID: PMC8702558 DOI: 10.3389/fncom.2021.743537] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2021] [Accepted: 11/09/2021] [Indexed: 11/17/2022] Open
Abstract
Sequential transitions between metastable states are ubiquitously observed in the neural system and underlying various cognitive functions such as perception and decision making. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand, fine recurrent neural networks trained with supervised machine learning methods can generate complex non-Markov sequences, but these sequences are vulnerable against perturbations and such learning methods are biologically implausible. How stable and complex sequences are generated in the neural system still remains unclear. We have developed a neural network with fast and slow dynamics, which are inspired by the hierarchy of timescales on neural activities in the cortex. The slow dynamics store the history of inputs and outputs and affect the fast dynamics depending on the stored history. We show that the learning rule that requires only local information can form the network generating the complex and robust sequences in the fast dynamics. The slow dynamics work as bifurcation parameters for the fast one, wherein they stabilize the next pattern of the sequence before the current pattern is destabilized depending on the previous patterns. This co-existence period leads to the stable transition between the current and the next pattern in the non-Markov sequence. We further find that timescale balance is critical to the co-existence period. Our study provides a novel mechanism generating robust complex sequences with multiple timescales. Considering the multiple timescales are widely observed, the mechanism advances our understanding of temporal processing in the neural system.
Collapse
Affiliation(s)
- Tomoki Kurikawa
- Department of Physics, Kansai Medical University, Hirakata, Japan
| | - Kunihiko Kaneko
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan.,Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Tokyo, Japan
| |
Collapse
|
5
|
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.
Collapse
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.
| |
Collapse
|
6
|
Zhang F, Huang T, Wu Q, Zeng Z. Multistability of delayed fractional-order competitive neural networks. Neural Netw 2021; 140:325-335. [PMID: 33895556 DOI: 10.1016/j.neunet.2021.03.036] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Revised: 02/27/2021] [Accepted: 03/24/2021] [Indexed: 10/21/2022]
Abstract
This paper is concerned with the multistability of fractional-order competitive neural networks (FCNNs) with time-varying delays. Based on the division of state space, the equilibrium points (EPs) of FCNNs are given. Several sufficient conditions and criteria are proposed to ascertain the multiple O(t-α)-stability of delayed FCNNs. The O(t-α)-stability is the extension of Mittag-Leffler stability of fractional-order neural networks, which contains monostability and multistability. Moreover, the attraction basins of the stable EPs of FCNNs are estimated, which shows the attraction basins of the stable EPs can be larger than the divided subsets. These conditions and criteria supplement and improve the previous results. Finally, the results are illustrated by the simulation examples.
Collapse
Affiliation(s)
- Fanghai Zhang
- School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, China.
| | - Tingwen Huang
- Science Program, Texas A&M University at Qatar, Doha, Qatar.
| | - Qiujie Wu
- School of Internet, Anhui University, Hefei, China.
| | - Zhigang Zeng
- School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, China.
| |
Collapse
|
7
|
Duan L, Zhang M, Zhao Q. Finite-time synchronization of delayed competitive neural networks with different time scales. JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2019. [DOI: 10.1080/02522667.2018.1453670] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Lian Duan
- School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China
- School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China
| | - Mengmeng Zhang
- School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China
| | - Qianjin Zhao
- School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China
| |
Collapse
|
8
|
|
9
|
Liu X, Yang C, Zhou L. Global asymptotic stability analysis of two-time-scale competitive neural networks with time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.07.047] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
10
|
Zhou L, Zhao Z. Exponential stability of a class of competitive neural networks with multi-proportional delays. Neural Process Lett 2015. [DOI: 10.1007/s11063-015-9486-6] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
11
|
Wang Y, Huang L. Global stability analysis of competitive neural networks with mixed time-varying delays and discontinuous neuron activations. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.11.016] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
12
|
Global dynamics of equilibrium point for delayed competitive neural networks with different time scales and discontinuous activations. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2013.07.026] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
13
|
Nie X, Cao J, Fei S. Multistability and instability of delayed competitive neural networks with nondecreasing piecewise linear activation functions. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2013.03.030] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
14
|
Xiaobing Nie, Jinde Cao. Multistability of Second-Order Competitive Neural Networks With Nondecreasing Saturated Activation Functions. ACTA ACUST UNITED AC 2011; 22:1694-708. [DOI: 10.1109/tnn.2011.2164934] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
15
|
|
16
|
An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays. Neural Comput Appl 2011. [DOI: 10.1007/s00521-011-0626-2] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
17
|
Xinsong Yang, Jinde Cao, Yao Long, Weiguo Rui. Adaptive Lag Synchronization for Competitive Neural Networks With Mixed Delays and Uncertain Hybrid Perturbations. ACTA ACUST UNITED AC 2010; 21:1656-67. [DOI: 10.1109/tnn.2010.2068560] [Citation(s) in RCA: 95] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
|
18
|
Local uniform stability of competitive neural networks with different time-scales under vanishing perturbations. Neurocomputing 2010. [DOI: 10.1016/j.neucom.2009.10.003] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
19
|
Gu H. Adaptive synchronization for competitive neural networks with different time scales and stochastic perturbation. Neurocomputing 2009. [DOI: 10.1016/j.neucom.2009.08.004] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
20
|
Min Wu, Fang Liu, Peng Shi, Yong He, Yokoyama R. Exponential Stability Analysis for Neural Networks With Time-Varying Delay. ACTA ACUST UNITED AC 2008; 38:1152-6. [DOI: 10.1109/tsmcb.2008.915652] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
|
21
|
Liu XG, Martin RR, Wu M, Tang ML. Global exponential stability of bidirectional associative memory neural networks with time delays. IEEE TRANSACTIONS ON NEURAL NETWORKS 2008; 19:397-407. [PMID: 18334360 DOI: 10.1109/tnn.2007.908633] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
In this paper, we consider delayed bidirectional associative memory (BAM) neural networks (NNs) with Lipschitz continuous activation functions. By applying Young's inequality and Hoelder's inequality techniques together with the properties of monotonic continuous functions, global exponential stability criteria are established for BAM NNs with time delays. This is done through the use of a new Lyapunov functional and an M-matrix. The results obtained in this paper extend and improve previous results.
Collapse
Affiliation(s)
- Xin-Ge Liu
- School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan 410083, China
| | | | | | | |
Collapse
|
22
|
Zhang L, Yi Z, Yu J. Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions. ACTA ACUST UNITED AC 2008; 19:158-67. [PMID: 18269947 DOI: 10.1109/tnn.2007.904015] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
This paper studies multiperiodicity and attractivity for a class of recurrent neural networks (RNNs) with unsaturating piecewise linear transfer functions and variable delays. Using local inhibition, conditions for boundedness and global attractivity are established. These conditions allow coexistence of stable and unstable trajectories. Moreover, multiperiodicity of the network is investigated by using local invariant sets. It shows that under some interesting conditions, there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly. Simulations are carried out to illustrate the theories.
Collapse
Affiliation(s)
- Lei Zhang
- Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic ScienceTechnology of China, Chengdu, China.
| | | | | |
Collapse
|
23
|
Meyer-Base A, Thummler V. Local and Global Stability Analysis of an Unsupervised Competitive Neural Network. ACTA ACUST UNITED AC 2008; 19:346-51. [DOI: 10.1109/tnn.2007.908626] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
|