Nonperturbative Analysis of Chaos Synchronization in Coupled Logistic Maps

抄録

We study chaos synchronization using a nonperturbative method, where coupled logistic maps x_n+1=f(x_n)+D[y_n+1-x_n+1]; y_n+1=f(y_n)+D[x_n+1-y_n+1] with f(x)=ax(1-x) are considered. We prove theoretically that any initial points eventually synchronize if D>(a-3)/2; (a>3), where mapping of the full phase space is considered instead of tracing an orbit of one initial point. Particularly when a=4, D>0.5 is the necessary and sufficient condition for the synchronization. A significant disadvantage inherent in a conventional linear stability theory is also discussed.