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Review and examples of non-Feigenbaum critical situations associated with period-doubling

By: Sataev, I.R.; Kuznetsov, A.P.; Kuznetsov, S.P.;

2005 / IEEE / 0-7803-9235-3

Description

This item was taken from the IEEE Conference ' Review and examples of non-Feigenbaum critical situations associated with period-doubling ' We review several critical situations, linked with period-doubling transition to chaos, which require using at least two-dimensional maps as models representing the universality classes. Each of them corresponds to a saddle solution of the two-dimensional generalization of Feigenbaum-Cvitanovic equation and is characterized by a set of distinct universal constants analogous to Feigenbaum's /spl alpha/ and /spl delta/. We present a number of examples (driven self-oscillators, coupled Henon-like maps, coupled driven oscillators, coupled chaotic self-oscillators), which manifest these types of behavior.