Roundoff-induced phenomena and diffusion processes: the 'premature' synchronisation of coupled maps

When considering the synchronisation of two identical coupled systems the t hreshold of stability of a synchronised state is determined by the sign of the largest transverse Lyapunov exponent. In this Letter, we report simple cases in which analytic representations for the threshold of stability of t he synchronised state are obtainable, but are not in agreement with numeric s. This phenomenon is roundoff induced, and is investigated for coupled ite rative maps that, in some cases, can be described as homogeneous diffusion processes. (C) 2000 Elsevier Science B.V. All rights reserved.