Nonlinear Dynamic Systems and Application to Lorenz Equation

We present the concept of the complexity radii of nonlinear dynamic system (NDS) with linear perturbations. In this paper we improve the algorithm of the complexity radii. As a "robust measure" of dynamic complexity of NDS, the complexity radii provide the tolerated parameter perturbation values of NDS without losing its dynamic complexity. As an application, the real complexity radii of Lorenz equation have been calculated. Numeric simulation results showed that the perturbed Lorenz equation still generates strange attractor if the norms of the corresponding parameter perturbation matrices were less that the complexity radii of the Lorenz equation