A novel criterion for unpredictable motions

FEN F., Fen M. O., AKHMET M.

Filomat, cilt.37, sa.18, ss.6151-6160, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 18
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2298/fil2318151t
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.6151-6160
  • Anahtar Kelimeler: Subject Classification, Unpredictable solution, Generalized synchronization, Auxiliary system approach, Conditional Lyapunov exponent, Poincar? chaos, Lorenz system
  • Gazi Üniversitesi Adresli: Evet

Özet

We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient conditions for the existence of unpredictable motions in the dynamics of the response system are provided. The theoretical results are exemplified for coupled autonomous systems in which the drive is a hybrid dynamical system and the response is a Lorenz system. The auxiliary system approach and conditional Lyapunov exponents are utilized to detect the presence of generalized synchronization.