A novel criterion for unpredictable motions

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

FILOMAT, vol.37, no.18, pp.6151-6160, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 18
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2318151t
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.6151-6160
  • Keywords: Subject Classification, Unpredictable solution, Generalized synchronization, Auxiliary system approach, Conditional Lyapunov exponent, Poincar? chaos, Lorenz system, GENERALIZED SYNCHRONIZATION, INVARIANT-MANIFOLDS, CHAOS
  • Middle East Technical University Affiliated: Yes

Abstract

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.