ON THE NONCONVERGENCE PROBLEM IN COMPUTING THE CAPACITY OF STRANGE ATTRACTORS

The convergence of box-counting algorithm for computing the capacity of strange attrac-tors is affected by the discretization procedure, because the period of the difference equations differs from that of the original ODE'S and, in addition, a damping factor appears. Simply decreasing the time-steps in the integration scheme not only costs more computer time, but also may deprive the convergence at all. The nonconvergence problem can be overcome by choosing at first a correct sampling interval. We give numerical evidence for what said above on the example of the periodically forced Brusselator.