Generalized practical stability of Hopfield-type neural networks differential equations
DOI: https://doi.org/10.3846/mma.2026.23045Abstract
This paper investigates the boundedness and practical stability properties of solutions for a class of neural differential equations inspired by Hopfield-type neural networks. Specifically, we develop a novel analytical framework that extends beyond traditional Lyapunov stability theory, Barbalat-type arguments, and fixed-point methods by relaxing common structural assumptions such as smoothness and global Lipschitz continuity. Our approach broadens the class of admissible systems to include nonlinearities with weaker growth conditions and time-varying perturbations that are not easily handled by classical techniques. Sufficient conditions are established to ensure the existence of a globally exponentially stable neighborhood of the origin, even in the presence of varying perturbation conditions. Furthermore, numerical examples are provided to demonstrate and validate the main result.
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equilibrium, Hopfield neural networks, generalized practical stability, boundednessHow to Cite
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
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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.