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Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments

Author

Listed:
  • Marat Akhmet

    (Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey)

  • Zakhira Nugayeva

    (Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan)

  • Roza Seilova

    (Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan)

Abstract

There are three principal novelties in the present investigation. It is the first time Cohen–Grossberg-type neural networks are considered with the most general delay and advanced piecewise constant arguments. The model is alpha unpredictable in the sense of electrical inputs and is researched under the conditions of alpha unpredictable and Poisson stable outputs. Thus, the phenomenon of ultra Poincaré chaos, which can be indicated through the analysis of a single motion, is now confirmed for a most sophisticated neural network. Moreover, finally, the approach of pseudo-quasilinear reduction, in its most effective form is now expanded for strong nonlinearities with time switching. The complexity of the discussed model makes it universal and useful for various specific cases. Appropriate examples with simulations that support the theoretical results are provided.

Suggested Citation

  • Marat Akhmet & Zakhira Nugayeva & Roza Seilova, 2025. "Alpha Unpredictable Cohen–Grossberg Neural Networks with Poisson Stable Piecewise Constant Arguments," Mathematics, MDPI, vol. 13(7), pages 1-27, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1068-:d:1620227
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    References listed on IDEAS

    as
    1. Kong, Fanchao & Ren, Yong & Sakthivel, Rathinasamy, 2021. "New criteria on periodicity and stabilization of discontinuous uncertain inertial Cohen-Grossberg neural networks with proportional delays," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Xiaoai Li, 2014. "Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Xiaoai Li, 2014. "Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, March.
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