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Impulsive effects on competitive neural networks with mixed delays: Existence and exponential stability analysis

Author

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  • Balasundaram, K.
  • Raja, R.
  • Pratap, A.
  • Chandrasekaran, S.

Abstract

In the proposed research work, the problem of dynamic analysis for a class of existence and global exponential stability of impulsive competitive neural networks (ICNNs) with multiple delays and effects of time scale parameter is investigated. Here the mixed delays include infinite distributed delay and discrete time multiple delays. Firstly, by means of non-linear Lipschitz measure (NLM) and some matrix inequality techniques, the existence and uniqueness of the network equilibrium point is proved, while by fabricating a suitable Lyapunov functional, some new brand of algebraic sufficient conditions is ensured to be globally exponentially stable in voice of linear matrix inequality (LMI). Finally, a numerical example with simulations are shown to illustrate the essence and merits of our obtained analytical results with some existing ones in the available literature.

Suggested Citation

  • Balasundaram, K. & Raja, R. & Pratap, A. & Chandrasekaran, S., 2019. "Impulsive effects on competitive neural networks with mixed delays: Existence and exponential stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 290-302.
    • Handle: RePEc:eee:matcom:v:155:y:2019:i:c:p:290-302
    DOI: 10.1016/j.matcom.2018.05.008
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    References listed on IDEAS

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    1. Esteves, Salete & Oliveira, José J., 2015. "Global asymptotic stability of nonautonomous Cohen–Grossberg neural network models with infinite delays," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 333-346.
    2. Maharajan, C. & Raja, R. & Cao, Jinde & Rajchakit, G. & Tu, Zhengwen & Alsaedi, Ahmed, 2018. "LMI-based results on exponential stability of BAM-type neural networks with leakage and both time-varying delays: A non-fragile state estimation approach," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 33-55.
    3. Zhang, Chunmei & Chen, Tianrui, 2018. "Exponential stability of stochastic complex networks with multi-weights based on graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 602-611.
    4. Raja, R. & Zhu, Quanxin & Senthilraj, S. & Samidurai, R., 2015. "Improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1050-1069.
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    Citations

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    Cited by:

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    2. Deng, Yunke & Huang, Chuangxia & Cao, Jinde, 2021. "New results on dynamics of neutral type HCNNs with proportional delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 51-59.
    3. Nirvin, Prasath & Rihan, Fathalla A. & Rakkiyappan, Rajan & Pradeep, Chandrasekar, 2022. "Impulsive sampled-data controller design for synchronization of delayed T–S fuzzy Hindmarsh–Rose neuron model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 588-602.
    4. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Iswarya, M. & Raja, R. & Cao, J. & Niezabitowski, M. & Alzabut, J. & Maharajan, C., 2022. "New results on exponential input-to-state stability analysis of memristor based complex-valued inertial neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 440-461.
    6. Aadhithiyan, S. & Raja, R. & Zhu, Q. & Alzabut, J. & Niezabitowski, M. & Lim, C.P., 2021. "Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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