Discrete Lyapunov functional for cyclic systems of differential equations with time-variable or state-dependent delay

2025/02/05 by István Balázs, Balázs, István, Ábel Garab +1 · 1 citation
Computer Science · Mathematics · #34K06 #34K11 #34K25 #34K43 #37C60 #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Control Systems and Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.03648

openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

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.

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