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Journal of Applied Nonlinear Dynamics 14(2) (2025) 463--481 | DOI:10.5890/JAND.2025.06.014

Walid Oukil

Faculty of Mathematics, University of Science and Technology Houari Boumediene, BP 32 EL ALIA 16111 Bab Ezzouar, Algiers, Algeria

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Abstract

This paper investigates the exponential stability of abstract mean field systems in their synchronized state. We analyze stability by studying the linearized system and demonstrate the existence of an exponentially stable invariant manifold. Our focus is on the equilibrium stability under synchronization. We provide a comprehensive analysis of both linear and nonlinear cases of the system. Additionally, we prove the existence of stable limit cycles and establish a relation between the dynamics in linear and nonlinear frameworks.

Acknowledgments

The author would like to thank the Editor for their support and the Reviewers for their valuable comments.

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