Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument

Date

2023-04-01

Author

Akhmet, Marat
Tleubergenova, Madina
Nugayeva, Zakhira

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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A new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neural networks. The existence and exponential stability of unique unpredictable and Poisson stable motions of the neural networks are proved. Due to the generalized piecewise constant argument, solutions are continuous functions with discontinuous derivatives, and, accordingly, Poisson stability and unpredictability are studied by considering the characteristics of continuity intervals. That is, the piecewise constant argument requires a specific component, the Poisson triple. The B-topology is used for the analysis of Poisson stability for the discontinuous functions. The results are demonstrated by examples and simulations.

Subject Keywords

exponential stability, generalized piecewise constant argument, inertial neural networks, Poincaré chaos, Poisson stable oscillations, Poisson triple, unpredictable input–outputs, unpredictable oscillations

URI

https://hdl.handle.net/11511/103531

Collections

Department of Mathematics, Article