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Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument
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Date
2022-09-01
Author
Akhmet, Marat
Tleubergenova, Madina
Seilova, Roza
Nugayeva, Zakhira
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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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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.