Proving the Convergence to Limit Cycles using Periodically Decreasing Jacobian Matrix Measures

2023/04/04 by Jawher Jerray, Laurent Fribourg, Jerray, Jawher +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Electrical engineering #Quantum chaos and dynamical systems #Systems and Control (eess.SY) #electronic engineering #information engineering #stochastic dynamics and bifurcation

paper · doi:10.48550/arxiv.2304.01691

openalex publication_date 2023/04/04 · openalex created_date 2023/04/07 · openalex updated_date 2026/07/28

Abstract

Methods based on "(Jacobian) matrix measure" to show the convergence of a dynamical system to a limit cycle (LC), generally assume that the measure is negative everywhere on the LC. We relax this assumption by assuming that the matrix measure is negative "on average" over one period of LC. Using an approximate Euler trajectory, we thus present a method that guarantees the LC existence, and allows us to construct a basin of attraction. This is illustrated on the example of the Van der Pol system.

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