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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)

- Diego Pazó
- Physical review. E, Statistical, nonlinear, and…
- 2005

In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter K(c). We obtain the asymptotic dependence of the order parameter above criticality: r-r(c)alpha(K - K(c))(2/3). For a finite population, we demonstrate… (More)

Rotating waves in cardiac muscle may be pinned to a heterogeneity, as it happens in superconductors or in superfluids. We show that the physics of electric field distribution between cardiac cells permits one to deliver an electric pulse exactly to the core of a pinned wave, without knowing its position, and even to locations where a direct access is not… (More)

- Diego Pazó, Michael A Zaks, Jürgen Kurths
- Chaos
- 2003

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)

Large communities of biological oscillators show a prevalent tendency to self-organize in time. This cooperative phenomenon inspired Winfree to formulate a mathematical model that originated the theory of macroscopic synchronization. Despite its fundamental importance, a complete mathematical analysis of the model proposed by Winfree—consisting of a large… (More)

- Ernest Montbrió, Diego Pazó, Jürgen Schmidt
- Physical review. E, Statistical, nonlinear, and…
- 2006

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)

- Diego Pazó, Ernest Montbrió
- Physical review. E, Statistical, nonlinear, and…
- 2006

We study the robustness of self-sustained oscillatory activity in a globally coupled ensemble of excitable and oscillatory units. The critical balance to achieve collective self-sustained oscillations is analytically established. We also report a universal scaling function for the ensemble's mean frequency. Our results extend the framework of the "aging… (More)

Controlling cardiac chaos is often achieved by applying a large damaging electric shock-defibrillation. It removes all waves, without differentiating reentries and normal waves, anatomical and functional reentries. Anatomical reentries can be removed by anti-tachycardia pacing (ATP) as well. But ATP requires the knowledge of the position of the reentry, and… (More)

- Ernest Montbrió, Diego Pazó
- Physical review letters
- 2011

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)

- Diego Pazó, Esteban Sánchez, Manuel A. Matias
- I. J. Bifurcation and Chaos
- 2001

In this contribution we report on a transition to high-dimensional chaos through three-frequency quasiperiodic behavior. The resulting chaotic attractor has a one positive and two null Lyapunov exponents. The transition occurs at the point at which two symmetry related threedimensional tori merge in a crisis-like bifurcation. The route can be summarized as:… (More)