Discrete Lyapunov functional for cyclic systems of differential equations with time-variable or state-dependent delay
Dynamical Systems
2025-10-10 v1
Abstract
We consider nonautonomous cyclic systems of delay differential equations with variable delay. Under suitable feedback assumptions, we define an (integer valued) Lyapunov functional related to the number of sign changes of the coordinate functions of solutions. We prove that this functional possesses properties analogous to those established by Mallet-Paret and Sell for the constant delay case and by Krisztin and Arino for the scalar case. We also apply the results to equations with state-dependent delays.
Cite
@article{arxiv.2502.03648,
title = {Discrete Lyapunov functional for cyclic systems of differential equations with time-variable or state-dependent delay},
author = {István Balázs and Ábel Garab},
journal= {arXiv preprint arXiv:2502.03648},
year = {2025}
}