Dynamics of a class of time-period strongly 2-cooperative system: integer-valued Lyapunov function and embedding property of limit sets

2024/01/16 by Gao, Mengmeng, Zhou, Dun · 1 citation
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.08137

Abstract

We construct an integer-valued Lyapunov function σ(⋅) for generalized negative cyclic feedback system; and prove that σ(⋅) on any ω-limit set which generated by Poincaré mapping of bounded solution of such strongly 2-cooperative system is constant. Therefore, the ω-limit can be continuously embedded into a compact subset of a two-dimensional plane. Finally, a dissipative condition is given to ensure that all orbits of such system are bounded.

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• Structural stability for the bidirectional cyclic negative feedback systems

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