Open AccessFrozen random patterns in a globally coupled discontinuous map lattices system
Author(s) -
Tan Hong-Fang,
Tao Jin,
Shi-Xian Qu
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.040507
Subject(s) - coupled map lattice , lyapunov exponent , attractor , statistical physics , chaotic , coupling (piping) , discontinuity (linguistics) , physics , coupling strength , mathematics , synchronization of chaos , mathematical analysis , computer science , condensed matter physics , materials science , control theory (sociology) , control (management) , artificial intelligence , metallurgy
A class of the characteristic collective dynamic behaviors, i.e., the frozen random patterns, in a globally coupled both-discontinuous-and-non-invertible-map lattices are studied. The coupling-strength dependences of the mean order parameters and the largest Lyapunov exponents are calculated and analyzed. The result shows that, given the initial values for the dynamical variables, the system will reach its complete or partial synchronization state when the coupling strength is beyond some critical value, where the frozen random pattern appears. These phenomena reveal that there are coexisting attractors in the system, and thus the structure and the distribution of the frozen random patterns sensitively depend on the choice of the initial dynamics variables. The interesting event is that the system can be modulated to some regular states of motion by the coupling among lattices even when the single maps are in the chaotic states, which may have some important applications in controlling chaos. The rich dynamical behaviors mentioned above are due to the interplay between the discontinuity and the non-invertibility in the map.