The Design And Analysis Of A New Hyperchaotic System

Chaos has been paid more attention increasingly as a proceeding project and science hotspot. The investigation of hyperchaos is a new subject based on chaotic system. Compared to chaotic system, hyperchaotic system has much more complex dynamical behaviour. System's randomness and indeterminacy has enhanced much, hence hyperchaos has much more extensive value in engineering application. For example, recent study indicates that, hyperchaotic signal is more difficult to predict by common methods such as rebuilding phase space, regress mapping, nonlinear predict, which are usually used for low-dimension chaos signal. So it has great application significance to design, implement and analyse hyperchaotic systems with at least two positive lyapunov exponents.Based on the research results of chaos and hyperchaos in theory, this paper has made detailed analysis of the generation methods and circuit implementation of hyperchaos. The paper includes five aspects as follows:1. Firstly, the definition, basic characteristic and analysis methods of chaotic and hyperchaotic systems are recommended. Basic means and conception of chaos, hyperchaos synchronization has also been mentioned. Based on the study of some classic chaotic and hyperchaotic systems, some program used for analyzing characteristic of chaotic system has been worked out, such as the program of drawing phase track figure, program of drawing bifurcation figure, program of calculating Lyapunov exponents and so on.2. The generalized Lorenz chaotic systems are studied detailedly in this paper. Using feedback control, the corresponding four-dimension generalized Lorenz hyperchaotic systems are gained.These hyperchaotic systems are also been analyzed theoretically here. Through many computer simulations, the rule using positive feedback control to construct four-dimension hyperchaotic system from third-order chaotic one is concluded, which called the positive feedback control method. Here, the form of the controller and where it effects have been discussed in detail. This positive feedback control method can be widely used in many chaotic systems, some other simulation are also given to prove so.3. A new third-order chaotic system is designed in this paper. By the positive feedback control method, a new four-dimension hyperchaotic system is gained. Characteristic of this new hyperchaotic system is studied in detail, including validating the hyperchaotic quality, analysing phase track, calculating Lyapunov exponents, drawing bifurcation figure and so on. Simulation results indicate that the dynamical behaviour of this hyperchaotic system is very complex.4. Hyperchaotic circuit is designed and implemented here. Meanwhile, experimental results of this circuit are also given——the phase track figure. Through computing the circuit parameters and analyzing model parameters in theory, consistency of experimental results and computer simulations is proved. Hyperchaotic circuit designed here has a simple structure as well as plenty kinds of dynamical behaviour, the parameters of it can also be easily debugged. Meanwhile, it can be observed easily and the characteristic of chaos and hyperchaos can be very expediently found out through this circuit. It can be imagining that this hyperchaotic circuit will be a good signal source for hyperchaotic application.5. Hyperchaotic synchronization is investigated here.Using many variables linear feedback control can realize the synchronization of hyperchaos.This experiment is prepared for the application of hyperchaotic in secrecy commucation.