Стійкість синхронізованих та кластерних станів у системі зв'язаних кусково-лінійних відображень

Анотація

Parameter regions for different types of stability of synchronized and clustered states are obtained for two interacting ensembles of globally coupled one-dimensional piecewise linear maps. We analyze strong (asymptotic) and weak (Milnor) stability of the synchronized state, as well as its instability. We found that the stability and instability regions in the phase space depend only on parameters of the individual skew tent map, and do not depend on the ensembles size. In the simplest non-trivial case of four coupled chaotic maps we obtain stability regions for coherent and two-cluster states. The regions appear to be large enough to provide an effective control of coherent and clustered chaotic regimes. Transition from desynchronization to synchronization is identified to be qualitatively different in smooth and piecewise linear models.