The Integer-valued Lyapunov Function for a Class of Strong 2-positive Systems
This article establishes an integer-valued Lyapunov function σ(·) for bidirectional negative cyclic feedback systems. The functionσ(·),defined on an open and dense subset in ℝn,represents the number of sign changes among the coordinates of an n-dimensional vector. By defining two integer-valued functions,σm(·) and σM(·),associated with σ(·) and utilizing their properties,it is demonstrated that σ(·) decays along the trajectories of solutions. At the same time,if the integer-valued Lyapunov function so defined satisfies orbital decay,then the corresponding linear system is a strong 2-positive system almost everywhere. σ(·) provides an effective research tool for further studying the structural stability and embedding prop-erties of limit sets for negative cyclic feedback systems,offering an important reference for a deeper understanding of the dynamics of such systems.
dynamical systemstrong 2-cooperative systemstrong 2-positive systeminteger-valued Lyapunov function
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