2006/09/15 by D. V. Senthilkumar, M. Lakshmanan, Jürgen Kurths +1 · 3 citations
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #nlin.CD
paper · pdf · doi:10.1103/physreve.74.035205
4 pages, 3 Figures (To appear in Physical Review E Rapid Communication)
arxiv created 2006/09/15 · openalex publication_date 2006/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase-coherent hyperchaotic attractors. In this paper we report identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a transformation of the attractors, and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piecewise linear and in Mackey-Glass time-delay systems.