Analysis of spurious synchronization with positive conditional Lyapunov exponents in computer simulations

Synchronization of chaotic systems has been a field of great interest and p otential applications. The necessary condition for synchronization is the n egativity of the largest conditional Lyapunov exponent. Some researches hav e shown that negativity of the largest conditional Lyapunov exponent is not a sufficient condition for high-quality synchronization in the presence of small perturbations. However, it was reported that synchronization can be achieved with positive conditional Lyapunov exponents based on numerical si mulations. In this paper, we first analyze the behavior of synchronization with positive conditional Lyapunov exponents in computer simulations of the synchronization of chaotic systems with various couplings, and demonstrate that synchronization is an outcome of finite precision in numerical simula tions. It is shown that such a numerical artifact is quite common and easil y occurs in numerical simulations, thus can be confusing and misleading. So me behavior and properties of the synchronized system with slightly positiv e conditional Lyapunov exponents can be understood based on the theory of o n-off intermittency. We also study the effects of finite precision on numer ical simulation of on-off intermittency. Special care should be taken in nu merical simulations of chaotic systems in order not to mistake numerical ar tifacts as physical phenomena. (C) 2000 Elsevier Science B.V. All rights re served.