title: Phase synchronization in time-delay systems.
abstract: 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.
authors.affiliation: Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli, 620 024, India.
authors.forename: D V
authors.initials: DV
authors.lastname: Senthilkumar
authors.forename: M
authors.initials: M
authors.lastname: Lakshmanan
authors.forename: J
authors.initials: J
authors.lastname: Kurths