Catálogo de publicaciones - libros

Previous chapters were mainly devoted to the investigation of synchronization effects inside one chain or network of coupled oscillators and rotators. In this chapter, phenomena of collective oscillations in a system of two coupled chains of identical limit-cycle oscillators are investigated [331, 351–353]. It is shown that a pair of coupled chains with different collective frequencies exhibit stable fronts between two possible asymptotic states: synchronous oscillations and oscillation death. The inhomogeneous states formed by the fronts persist at weak coupling between the oscillators in each chain due to the discrete space variable, thus providing conditions for the existence of localized structures. At stronger coupling, the interface between both the regions of the chains may propagate. Different examples of synchronization patterns and their dynamics are presented including nontrivial effects such as (1) synchronized clusters induced by disorder and (2) transitions from nonpropagation to propagation of fronts via intermittency.

Previous chapters are devoted to synchronization phenomena in ensembles of self-oscillatory systems. In this chapter we apply the synchronization theory presented before to describe in detail possible responses of one- and twodimensional excitable media on an external periodic force [392]. This study is especially motivated by the important finding in cardiology that ventricular fibrillation might arise from spiral wave chaos [393]. Ventricular fibrillation is potentially lethal arrhythmia that can result in sudden cardiac death, which is, for example, responsible for 250,000 deaths in the US each year [394].

In the previous chapters, we have demonstrated various synchronization phenomena in arrays of coupled deterministic oscillators. However, noise is inevitably present in experimental and natural systems. Therefore, it is of interest and importance to explore the effects of noise on the robustness of the synchronization process.

In the previous chapters we have considered synchronization of oscillators which have regular arrangement (1D arrays or 2D lattices) with the coupling extended to the nearest neighbors (local coupling), see Fig. 1.2, or global coupling among all the osicllators (e.g., Sects. 5.5, 10.9, 13.3.3 and 13.3.4). Such simple coupling topology of the oscillators is relevant to many experimental and natural situations.