Quasilinear systems with unpredictable relay perturbations

Fen M. O., FEN F.

TURKISH JOURNAL OF MATHEMATICS, vol.46, no.4, pp.1369-1383, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2105-108
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1369-1383
  • Keywords: Unpredictable solution, unpredictable sequence, quasilinear system, Poincare chaos, discontinuous right-, hand side, POINCARE CHAOS, EQUATIONS
  • TED University Affiliated: Yes


It is rigorously proven under certain assumptions that a quasilinear system with discontinuous right-hand side possesses a unique unpredictable solution. The discontinuous perturbation function on the right-hand side is defined by means of an unpredictable sequence. A Gronwall-Coppel type inequality is utilized to achieve the main result, and the stability of the unpredictable solution is discussed. Examples with exponentially asymptotically stable and unstable unpredictable solutions are provided.