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Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations

Author

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  • Gani Stamov

    (Department of Mathematical Physics, Technical University of Sofia, 8800 Sliven, Bulgaria)

  • Ivanka Stamova

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA)

  • George Venkov

    (Department of Mathematical Analysis and Differential Equations, Technical University of Sofia, 1000 Sofia, Bulgaria)

  • Trayan Stamov

    (Department of Machine Elements and Non-metallic Constructions, Technical University of Sofia, 1000 Sofia, Bulgaria)

  • Cvetelina Spirova

    (Department of Mathematical Physics, Technical University of Sofia, 8800 Sliven, Bulgaria)

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.

Suggested Citation

  • Gani Stamov & Ivanka Stamova & George Venkov & Trayan Stamov & Cvetelina Spirova, 2020. "Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations," Mathematics, MDPI, vol. 8(7), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1082-:d:379823
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    References listed on IDEAS

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    1. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    2. Xianghong Lai & Tianxiang Yao, 2013. "Exponential Stability of Impulsive Delayed Reaction-Diffusion Cellular Neural Networks via Poincaré Integral Inequality," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, March.
    3. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
    4. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    5. Stamov, Gani Tr. & Stamova, Ivanka M., 2014. "Integral manifolds for uncertain impulsive differential–difference equations with variable impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 90-96.
    6. Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.
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    1. Stamova, Ivanka & Stamov, Trayan & Stamov, Gani, 2022. "Lipschitz stability analysis of fractional-order impulsive delayed reaction-diffusion neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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