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

Marat Akhmet (), Zakhira Nugayeva and Roza Seilova
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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
Roza Seilova: Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan

Mathematics, 2025, vol. 13, issue 7, 1-27

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.

Keywords: Cohen–Grossberg type neural networks; alpha unpredictable neural networks; Poisson stable piecewise constant argument; method of pseudo-quasilinear reduction; method of included intervals; ultra Poincare chaos; alpha unpredictable oscillation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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