2021/10/30 by Mehmet Onur Fen, Fen, Mehmet Onur, Fatma Tokmak Fen +1
Engineering · Mathematics · #34A37 #34C10 #34C60 #Chaotic Dynamics (nlin.CD) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2111.01129
openalex publication_date 2021/10/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
It is rigorously proved that quasilinear impulsive systems possess\nunpredictable solutions when a perturbation generated by an unpredictable\nsequence is applied. The existence, uniqueness, as well as asymptotic stability\nof such solutions are demonstrated. The system under consideration is with\nregular moments of impulses, and for that reason a novel definition for\nunpredictable functions with regular discontinuity moments is provided. To show\nthe existence of an unpredictable solution a Gronwall type inequality for\npiecewise continuous functions is utilized. The theoretical results are\nsupported with an illustrative example.\n