EXTREME SENSITIVE DEPENDENCE ON PARAMETERS AND INITIAL CONDITIONS IN SPATIOTEMPORAL CHAOTIC DYNAMICAL-SYSTEMS

We investigate the sensitive dependence of asymptotic attractors on bo th initial conditions and parameters in spatio-temporal chaotic dynami cal systems. Our models of spatio-temporal systems are globally couple d two-dimensional maps and locally coupled ordinary differential equat ions. It is found that extreme sensitive dependence occurs commonly in both phase space and parameter space of these systems. That is, for a n initial condition and/or a parameter value that leads to chaotic att ractors, there are initial conditions and/or parameter values arbitrar ily nearby that lead to nonchaotic attractors. This indicates the occu rrence of an extreme type of fractal structure in both phase space and parameter space. A scaling exponent used to characterize extreme sens itive dependence on initial conditions and parameters is determined to be near zero in both phase space and parameter space. Accordingly, th ere is a significant probability of error in numerical computations in tended to determine asymptotic attractors, regardless of the precision with which initial conditions or parameters are specified. Consequent ly, fundamental statistical properties of asymptotic attractors cannot be computed reliably for particular parameter values and initial cond itions.