Model description of a chain of coupled dynamic systems near order-disorder phase transitions
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A method is suggested of phenomenological description of a chain of coupled systems, demonstrating during the variation of some parameter a transition from periodic to chaotic regimes through an infinite sequence of period doubling. The method consists of using models, chains of coupled, one-dimensional mappings. It is shown that from the point of view of chain behavior, following a large number of period doublings the coupling between the systems is a combination of two fundamental types of coupling; equality of the corresponding coupling coefficients for a chain and its models is the correspondence condition between them. A specific example is considered, a chain of parametrically excited nonlinear oscillators with dissipation.
KeywordsPhase Transition Dynamic System Couple System Model Description Nonlinear Oscillator
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