Existence of unpredictable solutions and chaos

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AKHMET M., Fen M. O.

TURKISH JOURNAL OF MATHEMATICS, cilt.41, sa.2, ss.254-266, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 2
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/mat-1603-51
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.254-266
  • Anahtar Kelimeler: Poincare chaos, unpredictable function, Poisson stability, Bebutov dynamical system, quasilinear differential equation, chaos control, LI-YORKE CHAOS, DYNAMIC-SYSTEMS, GENERATION, SICNNS
  • TED Üniversitesi Adresli: Evet

Özet

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.