Existence of unpredictable solutions and chaos

AKHMET M., Fen M. O.

TURKISH JOURNAL OF MATHEMATICS, vol.41, no.2, pp.254-266, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.3906/mat-1603-51
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.254-266
  • Keywords: Poincare chaos, unpredictable function, Poisson stability, Bebutov dynamical system, quasilinear differential equation, chaos control, LI-YORKE CHAOS, DYNAMIC-SYSTEMS, GENERATION, SICNNS
  • Middle East Technical University Affiliated: Yes

Abstract

Recently we introduced the concept of Poincare chaos. In the present paper, by means of the Bebutov dynamical system, an unpredictable solution is considered as a generator of the chaos in a quasilinear system. The results can be easily extended to different types of differential equations. An example of an unpredictable function is provided. A proper irregular behavior in coupled Duffing equations is observed through simulations.