Delay-induced synchronization phenomena in an array of globally coupled logistic maps
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We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized states in which the elements of the array evolve along a periodic orbit of the uncoupled map, while the spatial correlation along the array is such that an individual map sees all other maps in his present, current, state. For values of the nonlinear parameter such that the uncoupled maps are chaotic, time-delayed mutual coupling suppresses the chaotic behavior by stabilizing a periodic orbit that is unstable for the uncoupled maps. The stability analysis of the synchronized state allows us to calculate the range of the coupling strength in which global synchronization can be obtained.
CitationMartí, A.C.; Masoller, C. Delay-induced synchronization phenomena in an array of globally coupled logistic maps. "Physical review E: statistical, nonlinear, and soft matter physics", Maig 2003, vol. 67, núm. 5, p. 056219-1-056219-6.