New existence and exponential stability results for periodic solutions in recurrent neural networks with generalized piecewise constant delay via coincidence degree theory
DOI: https://doi.org/10.3846/mma.2026.25296Abstract
The present work investigates recurrent neural systems incorporating generalized piecewise constant delay, with particular emphasis on establishing periodic behaviors and verifying their exponential convergence on a global scale. The existence of periodic solutions is established via Mawhin’s coincidence degree in combination with sharp a priori estimates, while uniqueness and exponential attractivity are derived through a Lyapunov functional approach supported by differential inequalities adapted to the delay structure. The obtained criteria are concise, verifiable, and applicable in practice. Representative computational experiments are provided to substantiate the analytical findings.
Keywords:
recurrent neural networks, generalized piecewise constant delay, periodic solutions, coincidence degree theory, global exponential stability, method of Lyapunov functionsHow to Cite
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.