Compartmental Poisson Stability in Non-autonomous Differential Equations

Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek

doi:10.1007/978-3-031-06632-0_1

Cited by 1 publication

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“…That is, we need a special kappa property [ 35 ], which establishes a correspondence between periodicity and the unpredictability. The existence of such factors should be due to the higher possibility of the selection of the triple

, when they satisfy

property [ 34 ], and in addition, the kappa property must be fulfilled [ 35 , 36 , 37 , 38 ]. In this paper, we utilize a stronger state when this triple is a Poisson triple, which is more comfortable in applications.…”

Section: Preliminariesmentioning

confidence: 99%

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

Akhmet

Tleubergenova

Nugayeva

2023

Entropy

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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.

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, when they satisfy

Section: Preliminariesmentioning

confidence: 99%