Synchronization in a population of globally coupled chaotic oscillators (original) (raw)
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The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters , such as Lyapunov exponents, that help predict the system's transitions into globally organized states. However, the local, microscopic, description of this emergent process continues to elude us. Here we show that at the microscopic level, synchronization is captured through a gradual process of topological adjustment in phase space, in which the strange attractors of the two coupled systems continuously converge, taking similar form, until complete topological synchronization ensues. We observe the local nucleation of topological synchronization in specific regions of the system's attractor, providing early signals of synchrony, that appear significantly before the onset of complete synchronization. This local synchronization initiates at the regions of the attractor characterized by lower expansion rates, in which the chaotic trajectories are least sensitive to slight changes in initial conditions. Our findings offer a fresh and novel description of synchronization in chaotic systems, exposing its local embryonic stages that are overlooked by the currently established global analysis. Such local topological synchronization enables the identification of configurations where prediction of the state of one system is possible from measurements on that of the other, even in the absence of global synchronization.
Synchronization in small assemblies of chaotic systems
Physical Review E, 1996
In this paper we investigate the behavior of small networks of van der Pol-Duffing chaotic oscillators that are connected through local, although not weak, coupling through a recently introduced ͓Phys. Rev. E 52, R2145 ͑1995͔͒ extension of the Pecora-Carroll synchronization method. The method allows one to design a variety of settings with different ways of connecting a number of low-dimensional circuits. It is shown that a variety of different behaviors can be obtained, depending, among other factors, on the symmetry of the connections and on whether the oscillators are identical or different. One may cite the emergence of coherent behavior ͑a single cluster͒, either chaotic or periodic, as stemming just from interaction among the different chaotic units, although several coexisting clusters are found for other settings.