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We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto a cylindrical phase space. Starting from a normal form that describes the nonequilibrium Ising-Bloch bifurcation in… (More)

We investigate the effects of a time-delayed all-to-all coupling scheme in a large population of oscillators with natural frequencies following a bimodal distribution. The regions of parameter space corresponding to synchronized and incoherent solutions are obtained both numerically and analytically for particular frequency distributions. In particular, we… (More)

We propose a procedure to distinguish quasiperiodic from chaotic orbits in short-time series, which is based on the recurrence properties in phase space. The histogram of the return times in a recurrence plot is introduced to disclose the recurrence property consisting of only three peaks imposed by Slater's theorem. Noise effects on the statistics are… (More)

We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one due to the shallowness of the central dip. Here we show that proximity to the… (More)

Large ensembles of heterogeneous oscillators often exhibit collective synchronization as a result of mutual interactions. If the oscillators have distributed natural frequencies and common shear (or nonisochronicity), the transition from incoherence to collective synchronization is known to occur at large enough values of the coupling strength. However,… (More)

An increase of the coupling strength in the system of two coupled Rössler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of… (More)

Phase synchronization is shown to occur between opposite cells of a ring consisting of chaotic Lorenz oscillators coupled unidirectionally through driving. As the coupling strength is diminished, full phase synchronization cannot be achieved due to random generation of phase jumps. The brownian dynamics underlying this process is studied in terms of a… (More)

Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are… (More)

We analyze the synchronization dynamics of a model obtained from the phase reduction of the mean-field complex Ginzburg-Landau equation with heterogeneity. We present exact results that uncover the role of dissipative and reactive couplings on the synchronization transition when shears and natural frequencies are independently distributed. As it occurs in… (More)

- Hayato Chiba, Diego Pazó
- 2009

When the natural frequencies are allocated symmetrically in the Kuramoto model there exists an invariant torus of dimension [N/2] + 1 (N is the population size). A global phase shift invariance allows to reduce the model to N − 1 dimensions using the phase differences, and doing so the invariant torus becomes [N/2]-dimensional. By means of perturbative… (More)