Replication of chaos

AKHMET M., Fen M. O.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.18, no.10, pp.2626-2666, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 10
  • Publication Date: 2013
  • Doi Number: 10.1016/j.cnsns.2013.01.021
  • Journal Name: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2626-2666
  • Keywords: Replication of chaos, Hyperbolic set of functions, Chaotic set of functions, Period-doubling cascade, Devaney chaos, Li-Yorke chaos, Intermittency, Chaotic attractor, Chaos control, Shil'nikov orbits, The double-scroll Chua's attractor, Quasiperiodicity, Morphogenesis of chaos, LI-YORKE CHAOS, TRANSITION, EQUATION, CIRCUIT, SYSTEMS, SYNCHRONIZATION, HYPERCHAOS, ATTRACTORS
  • TED University Affiliated: No

Abstract

We propose a rigorous method for replication of chaos from a prior one to systems with large dimensions. Extension of the formal properties and features of a complex motion can be observed such that ingredients of chaos united as known types of chaos, Devaney's, Li-Yorke and obtained through period-doubling cascade. This is true for other appearances of chaos: intermittency, structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. That is why we identify the extension of chaos through the replication as morphogenesis.