Chaotic synchronization of mutually coupled nonchaotic systems

A chaotic dynamical system is one in which the system obeys deterministic laws but its future and past are difficult to predict. In this study, we observed and discussed the behavior of orbits of coupled two nonchaotic dynamical systems when they are coupled. As a result, a chaotic synchronization phenomenon, in which the orbits of the two dynamical systems synchronize completely with chaotic natures, was observed under certain conditions. We clarified the conditions under which the phenomenon occurs by analytically deriving the conditional Lyapunov exponent, Cauchy Laws with ergodic theory.