Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument

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2022-09-01

Author

Akhmet, Marat
Tleubergenova, Madina
Seilova, Roza
Nugayeva, Zakhira

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In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.

Subject Keywords

impulsive shunting inhibitory cellular neural networks, symmetry of impulsive and differential parts, continuous and impact activations, generalized piecewise constant argument, method of included intervals, continuous and discontinuous Poisson stable inputs and outputs, GLOBAL EXPONENTIAL STABILITY, ALMOST-PERIODIC SOLUTIONS, DIFFERENTIAL-EQUATIONS, NEGATIVE CAPACITANCE, EXISTENCE

URI

https://hdl.handle.net/11511/101037

Journal

SYMMETRY-BASEL

DOI

https://doi.org/10.3390/sym14091754

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, M. Tleubergenova, R. Seilova, and Z. Nugayeva, “Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument,” SYMMETRY-BASEL, vol. 14, no. 9, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/101037.