Control Chaos In Hamiltonian Systems

In this thesis, we summarize our recent contribution to controlling of chaos of conservative systems. Our new results are: 1. We have discussed periodic pulse method to controlling a chaotic systems. An essential condition for controlling dissipative systems has been via an analysis of the dynamical character of open-loop periods pulses, at the same time, we extend the applyed range of the periods pulses. After a close-loop pertubation is added, a method for controlling global chaotic in two-dimensional Hamiltonian systems is proposed in a model of the standard map. The method is robust under the presence of weak external noise. By the way, the basin of attractors hase been discussed. 2. We present a method which allowing one to employ another external kicks with strength K and delay q to control the global stochasticity in two-dimensional Hamiltonian systems, here we use a model of the standard map, the control here means that the chaotic state will be able to changed in the entire angular momentum interval [梒tD,ct~] at will. Through the action of periodically external kicks to a standard map, a new type of spatial intermittency, we term it as chaotic wave, appears. Especially, split the strength of the kicks of originally standard map into two parts with delay q ?1, a region where the KAM tori are reconstructed, and such KAM tori always can be found no matter how large the strength is. Results show that the behaviors of the controlled system are sensitive to the change of delay ~ and obtuse to the change of controlling kicks strength K? 3. Some new type of two freedom Hamiltonian system models have been provided. One of them, one-dimensional periodic driven I-Lamiltonian system (not harmonic), its characteristics have been discussed Chaotic dynamics in a driven oscillator is controlled using an adjustable, passive limiter (a weight for the oscillator), the chaotic trajectories of the conservative system can be controlled to some of low periodic (or low energy) orbits. The results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. 4 At the first, we have discussed the chaotic dynamical character of periodic driven harmonious osillator method (Henon map). Secondly, controlling of chaos has been discussed. We have extended the controlling method which has been presented in chap. 3, another external kicks are conservative. The proportion of regular regions is obvious increase after the systems are controlled.