Stability of Periodic Solutions for Hysteresis-Delay Differential\n Equations

2017/10/20 by Pavel Gurevich, Gurevich, Pavel, Eyal Ron +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #34C25 #34K13 #37C27 #47J40 #Advanced Mathematical Modeling in Engineering #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Piezoelectric Actuators and Control

paper · pdf · doi:10.48550/arxiv.1710.07444

openalex publication_date 2017/10/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We study an interplay between delay and discontinuous hysteresis in dynamical\nsystems. After having established existence and uniqueness of solutions, we\nfocus on the analysis of stability of periodic solutions. The main object we\nstudy is a Poincar 'e map that is infinite-dimensional due to delay and\nnon-differentiable due to hysteresis. We propose a general functional framework\nbased on the fractional order Sobolev--Slobodeckij spaces and explicitly obtain\na formal linearization of the Poincar 'e map in these spaces. Furthermore, we\nprove that the spectrum of this formal linearization determines the stability\nof the periodic solution and then reduce the spectral analysis to an equivalent\nfinite-dimensional problem.\n

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