Li-Yorke Chaos in Hybrid Systems on a Time Scale

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AKHMET M., Fen M. O.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, cilt.25, sa.14, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 14
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1142/s0218127415400246
  • Dergi Adı: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Li-Yorke chaos, dynamic equations on time scales, proximality, frequent separation, Duffing equation, hybrid systems, DIFFERENTIAL-EQUATIONS, DYNAMICAL SYNTHESIS
  • TED Üniversitesi Adresli: Hayır

Özet

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.