Stability of Asymmetric Cluster States in Globally Coupled Maps
نویسنده
چکیده
Globally coupled maps can exhibit interesting dynamics. We construct stable cluster states, for which the variables divide into two separately synchronized populations. These stable states coexist with stable synchronized states and explain some observations in the literature.
منابع مشابه
Periodicity manifestations in the turbulent regime of the globally coupled map lattice
We revisit the globally coupled map lattice. We show that in the so called turbulent regime various periodic cluster attractor states are formed, even though the coupling between the maps are very small relative to the nonlinearity in the element maps. Most outstanding is a maximally symmetric three cluster attractor in period-3 motion, due to the foliation of the period-3 window of the element...
متن کاملLong transients and cluster size in globally coupled maps
– We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the ordered phase of these systems. The transient times necessary to reach the asymptotic states can be very long, especially very near the transition line separatin...
متن کاملBifurcations in Globally Coupled Chaotic Maps
We propose a new method to investigate collective behavior in a network of globally coupled chaotic elements generated by a tent map. In the limit of large system size, the dynamics is described with the nonlinear FrobeniusPerron equation. This equation can be transformed into a simple form by making use of the piecewise linear nature of the individual map. Our method is applied successfully to...
متن کاملStabilization of Causally and Non–Causally Coupled Map Lattices
Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of “causal” coupling (to spatially distant past states) or “non-causal” coupling (to spatially distant simultaneous states). In this contribution we show that globally stabl...
متن کاملMutual synchronization and clustering in randomly coupled chaotic dynamical networks.
We introduce and study systems of randomly coupled maps where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally coupled maps) until a certain critical threshold for the connectivity is reached. We further show that not only the average connectivity, but also the architecture ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003