Estimates of the Lyapunov Dimension of Attractors for Generalized Rössler Systems
Generalization of one of the classical Rцssler systems are considered. It is shown that, to estimate the dimensions of the attractors of these systems, Lyapunov functions can be effectively used. By using these functions, estimates of the Lyapunov dimensions of the attractors of generalized Rцssler systems are obtained. For the local Lyapunov dimensions of the attractors of these systems, exact expressions are given. In the limit case, the coincidence of the topological, Hausdorff, fractal, and Lyapunov dimensions of attractors is proved. It is shown that, for standard values of Rцssler parameters, the values given by expressions for local Lyapunov dimensions at zero coincide with those obtained in numerical experiments.