Experimental And Theoretic Study On Controlling Chaos And Hyperchaos Systems

Nowadays, chaos control has been intensively studied within physics, mathematics and so on. It has been realized that chaos control has great potential in many technological disciplines. As a main research method, circuits experiment have been integrated with theoretic analysis and numerical calculation, and we have obtained sufficient and correct results of the problems discussed in the paper. At first, this paper presents a symbolic method for chaos controller design based on the theory of controlling chaos by limiting amplitude. Some stabilized different periodic orbits were obtained, by thresholding just one variable. Experimental results of circuit and numerical simulation have demonstrated that this method of chaos control is effective. The controller is directly constructed by analytic formula without knowing unknown bounds about uncertain parameters in advance. The simplicity of this controller entailing no run-time computation, and the ease and rapidity of switching between different targets it offers, suggusts a potent tool for chaos based applications. In the second place, we show how stroboscopic threshold mechanisms can be effectively employed to obtain a wide range of stable cyclic behavior from chaotic systems, by simply varying the frequency of control. We demonstrate the success of the scheme in a prototypical one-dimensional map, as well as in a two-dimensional hyperchaos system. It is evident that thresholding is capable of yielding exact limit cycles of varying periods and geometries when implemented at different intervals. This suggests a simple and potent mechanism for selecting different regular temporal patterns from chaotic dynamics. In the third place , the control of a two dimensional discrete system –Henon map by means of time delayed variable feedback has been realized in an electronic circuit . The complex behaviours in the circuit and the various stabilized periodic states in the controlled circuit are in good agreement with the results obtained by analyzing theoretically and simulating numerically. In addition ,the experimental results confirm that it is effective to control chaos by using the method of improved time delayed variable feedback. Finally, a new method for controlling chaos is used , which is based on the method of prediction chaos control . We demonstrate the success in rapidly controlling different chaotic electrical circuits, including a Henon map circuit and a hyperchaotic circuit,onto stable fixed points and limit cycles of different periods. Our theoretical analysis and numerical simulation results have demonstrated that this control strategy works very effectively. The results we have achieved on controlling and chaos and hyperchaos systems via circuits experiments, and circuits simulation will undoubtedly provide important experimental guide for the practical application of controlling chaos system.