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Global Asymptotic Synchronization of a Class of BAM Neural Networks with Time Delays via Integrating Inequality Techniques

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Abstract

In this paper, the authors are concerned with global asymptotic synchronization for a class of BAM neural networks with time delays. Instead of using Lyapunov functional method, LMI method and matrix measure method which are recently widely applied to investigating global exponential/ asymptotic synchronization for neural networks, two novel sufficient conditions on global asymptotic synchronization of above BAM neural networks are established by using a kind of new study method of global synchronization: Integrating inequality techniques. The method and results extend the study of global synchronization of neural networks.

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References

  1. Kosko B, Adaptive bidirectional associative memories, Appl. Opt., 1987, 26: 4947–4960.

    Article  Google Scholar 

  2. Kosko B, Bidirectional associative memories, IEEE Trans. Syst. Man Cybern., 1983, 18: 49–60.

    Article  MathSciNet  Google Scholar 

  3. Ke Y Q and Miao C F, Stability and existence of periodic solutions in inertial BAM neural networks with time delay, Neural Comput. and Applic., 2013, 23(3–4): 1089–1089.

    Google Scholar 

  4. Zhang Z Q and Quan Z Y, Global exponential stability via inequality technique for inertial BAM neural networks with time delays, Neurocomputing, 2015, 151: 1316–1326.

    Article  Google Scholar 

  5. Qi J T, Li C D, and Huang T W, Stability of inertial BAM neural networks with time-varying delay via impulsive control, Neurocomputing, 2015, 161: 162–167.

    Article  Google Scholar 

  6. Zhang Z Q and Liu K Y, Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales, Neural Networks, 2011, 24(5): 427–439.

    Article  Google Scholar 

  7. Zhang Z Q, Cao J D, and Zhou D M, Novel LMI-based condition on global asymptotic stability for a class of Cohen-Grossberg BAM networks with extended activation functions, IEEE Trans. on Neural Networks and Learning System, 2014, 25(6): 1161–1172.

    Article  Google Scholar 

  8. Tu Z W, Ding N, Li L L, et al., Adaptive synchronization of memristive neural networks with time-varying delays and reaction-diffusion term, Applied Mathematics and Computation, 2017, 311: 118–128.

    Article  MathSciNet  Google Scholar 

  9. He W L and Cao J D, Exponential synchronization of chaotic neural networks: A matrix measure approach, Nonlinear Dyn., 2009, 55: 55–65.

    Article  MathSciNet  Google Scholar 

  10. Yi C B, Feng J W, Wang J Y, et al., Synchronization of delayed neural networks with hybird coupling via partial mixed pinning impulsive control, Applied Mathematics and Computation, 2017, 312: 78–90.

    Article  MathSciNet  Google Scholar 

  11. Zhang Z M, He Y, Wu M, et al., Exponential synchronization of chaotic neural networks with timevarying delay via intermittent output feedback approach, Applied Mathematics and Computation, 2017, 314: 121–132.

    Article  MathSciNet  Google Scholar 

  12. Li R X, Cao J D, Ahmad Alsaedi, et al., Exponential and fixed synchronization of Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms, Applied Mathematics and Computation, 2017, 313: 37–51.

    Article  MathSciNet  Google Scholar 

  13. Zhang Z Q and Ren L, New sufficient conditions on global asymptotic stability of inertial delayed neural networks by using integration inequality techniques, Nonlinear Dynamics, 2019, 95: 905–917.

    Article  Google Scholar 

  14. Cao J D and Wan Y, Matrix measure strategies for stability and synchronization of inertial BAM neural networks with time delays, Neural Networks, 2014, 53: 165–172.

    Article  Google Scholar 

  15. Prakash M, Balasubramaniam P, and Lakshmanan S, Synchronization of Markovian jumping inertial neural networks and its applications in image encryption, Neural Networks, 2016, 83: 86–93.

    Article  Google Scholar 

  16. Hu J Q, Cao J D, Abdulaziz Alofi, et al., Pinning synchronization of coupled inertial delayed neural networks, Cognitive Neurodynamics, 2015, 9(3): 341–350.

    Article  Google Scholar 

  17. Li Y and Li C D, Matrix measure strategies for stabilization and synchronization of delayed BAM neural networks, Nonlinear Dyn., 2016, 84: 1759–1770.

    Article  MathSciNet  Google Scholar 

  18. Cao J D and Wan Y, Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays, Neural Networks, 53: 165–172.

  19. Mathiyalagan K, Park Ju H, and Sakthivel R, Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities, Applied Mathematics and Computation, 2015, 259: 967–979.

    Article  MathSciNet  Google Scholar 

  20. Ge J H and Xu J, Synchronization and synchronized periodic solution in a simplified five-neuron BAM neural network with delays, Neurocomputing, 2011, 74(6): 993–999.

    Article  Google Scholar 

  21. Zhang W Y and Li J M, Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions, Boundary Value Problem, 2012, 2012: 2.

    Article  MathSciNet  Google Scholar 

  22. Kuang J C, Applied inequalities, Shandong Science and Technology Press, 3rd Edition, Qingdao, 2004.

    Google Scholar 

  23. Xia J W, Chen G L, and Sun W, Extended dissipative analysis of generalized Markovian switching neural networks with two delay components, Neurocomputing, 2017, 260(9): 275–283.

    Article  Google Scholar 

  24. Chen G L, Xia J W, and Zhang G M, Improved passivity analysis for neural networks with Markovian jumping parameters and interval time-varying delays, Neurocomputing, 2015, 155: 253–260.

    Article  Google Scholar 

  25. Sun J, Han Q L, Chen J, et al., Less conservative stability criteria for linear systems with interval time-varying delays, International Journal of Robust and Nonlinear Control, 2015, 25(4): 475–485.

  26. Sun J and Chen J, A survey on Lyapunov-based methods for stability of linear time-delay systems, Frontiers of Computer Science, 2017, 11(4): 555–567.

    Article  Google Scholar 

  27. Zhang Z Q and Cao J D, Periodic solutions for complex-valued neural networks of neutral type by combining graph theory with coincidence degree theory, Advances in Difference Equations, 2018, 2018: 261.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Tourism College of Beijing Union University, Beijing, 100101, China

    Feng Lin

  2. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Zhengqiu Zhang

Authors
  1. Feng Lin
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  2. Zhengqiu Zhang
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Correspondence to Feng Lin or Zhengqiu Zhang.

Additional information

This paper was recommended for publication by Editor SUN Jian.

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Lin, F., Zhang, Z. Global Asymptotic Synchronization of a Class of BAM Neural Networks with Time Delays via Integrating Inequality Techniques. J Syst Sci Complex 33, 366–382 (2020). https://doi.org/10.1007/s11424-019-8121-4

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  • DOI: https://doi.org/10.1007/s11424-019-8121-4

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