Unpredictability in Quasilinear Non-Autonomous Systems with Regular Moments of Impulses

Fen M. O., Tokmak Fen F.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.20, no.4, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1007/s00009-023-02401-6
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Impulsive system, discontinuous unpredictable solution, regular impulse moments, unpredictable sequence, asymptotic stability
  • TED University Affiliated: Yes

Abstract

The dynamics of quasilinear systems with regular moments of impulses is investigated when a perturbation generated by an unpredictable sequence is applied. The existence, uniqueness, as well as asymptotic stability of unpredictable solutions are proved making benefit of a novel definition regarding regular discontinuity moments. To achieve the main result a Gronwall type inequality for piecewise continuous functions is utilized. The theoretical results are supported with an illustrative example. This is the first time in the literature that the existence of unpredictable solutions is demonstrated for impulsive systems comprising periodic terms and regular moments of impulses.