Li-Yorke Chaos in Hybrid Systems on a Time Scale

Creative Commons License

AKHMET M., Fen M. O.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, vol.25, no.14, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 14
  • Publication Date: 2015
  • Doi Number: 10.1142/s0218127415400246
  • Journal Name: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Li-Yorke chaos, dynamic equations on time scales, proximality, frequent separation, Duffing equation, hybrid systems, DIFFERENTIAL-EQUATIONS, DYNAMICAL SYNTHESIS
  • TED University Affiliated: No

Abstract

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.