Related papers: Phase-flip bifurcation and synchronous transition …
Auxiliary system approach and various nearest neighbor methods are widely used to detect generalized synchronization in non-identical coupled systems. These methods generally give contradictory results. Therefore one method alone is not…
Synchronization in an array of mutually coupled systems with a finite time-delay in coupling is studied using Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by…
The main aim of this comment is to emphasize that the conditional Lyapunov exponents play an important role in distinguishing between intermittent and persistent synchronization, when the analytic criteria for asymptotic stability are not…
Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56},…
We analyze the desynchronization bifurcation in the coupled R\"ossler oscillators. After the bifurcation the coupled oscillators move away from each other with a square root dependence on the parameter. We define system transverse Lyapunov…
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay $\tau_1$ and coupling…
Phase synchronization in unidirectionally coupled Ikeda time-delay systems exhibiting non-phase-coherent hyperchaotic attractors of complex topology with highly interwoven trajectories is studied. It is shown that in this set of coupled…
A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical…
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 article…
We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that…
The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase…
We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic…
Transitions between inverse anticipatory, inverse complete and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also shown…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
We rigorously show that dissipatively driven Frenkel-Kontorova models with either uniform or time-periodic driving asymptotically synchronize for a wide range of initial conditions. The main tool is a new Lyapunov function, as well as a 2D…
We numerically study the synchronization of two nonidentical pendulum motions, pivoting on a common movable frame in the point of view of the dynamic phase transition. When the difference in the pendulum lengths is not too large, it is…
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for…
The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and…
We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are…
We investigate a system of four nearest neighbour bidirectional coupled phase oscillators of dissimilar initial frequencies in a ring at the changeover into a synchronizing state. There are twenty four permutations upon assigning the…