UNCERTAINTIES IN DETERMINISTIC DYNAMICAL SYSTEMS AND THE COHERENCE OF STOCHASTIC DYNAMICAL SYSTEMS

摘要

The uncertainties arising with the boundary crisis which destroys the Wada basin boundaries in the deterministic Henon map are investigated in this work. It is shown that the region of disappearing chaotic attractor and its basin become a part of the new basin boundary, and then a complex deterministic evolution follows. Meanwhile, the effect of noise to the qualitative structure of the system is studied. The small noise can hold the Wada property, but noise larger than can destroy one attractor and therefore the Wada property is disappeared. Secondly, we study the Duffing equation with uncertainty of a parameter. A kind of linear feedback is used to make this system resist large degree of uncertainty.