The Emulation And Synchronization Of Two New Chaotic Systems

Chaos control and synchronization are the frontier problems in nonlinear dynamics research. Nowadays, the research about application of chaos is developed from merely control and suppression to effective utilization. Scientists from all over the world have found many practice and potential application of chaos. Panasonic Corporation has invented microwave NNA724M with a device of'chaos defroster', it sharply cuts the defrosting time; designing the orbit of space vehicle according to the chaotic mechanism of astrodynamics, so it can reduce the loss of fuel and prolong the working period; improving the efficiency of liquid mixing according to chaotic theory; improving the treatment of Parkinson syndrome. Chaotic dynamics, with its natural randomness, has become a hot spot in communication and signal processing. However, the application of chaos cannot be isolated from chaotic systems/chaotic circuits. To serve this purpose, the paper present two new chaotic systems, realize them by using circuit emulation, and synchronize them by adaptive control and fuzzy control.Briefly review the research history of chaotic dynamics, introduce three definitions of chaos, several basic characters and methods in the research of chaos, such as Lyapunov exponents, power spectrum, Poincarémap, strange attractor. A few stability theories are proposed and prepared for the further research of chaos control and chaos synchronization.Present a new 3D chaotic system, analyze its basic dynamical characters, and obtain its Poincarémap, Lyapunov spectrum and bifurcation picture using numerical methods. It is a chaotic system via the analysis above. Then design a circuit according to the equation of the system, paving the way to its future application. Construct a new 4D hyperchaotic system, analyze its basic dynamical characters, and obtain its Lyapunov spectrum and bifurcation picture using numerical methods. Then design a circuit to realize this system. Moreover, an adaptive control method and a parameter update rule of unknown parameters based on Lyapunov stability theory are introduced to synchronize these two systems. Finally, the results are verified by the numerical simulation.Fuzzify the 4D hyperchaotic system according to TS theory, synchronize two systems according to Lyapunov stability theory. Design a controller to transmit a signal using two systems, even they have the different parameters. Finally, the results are verified by the numerical simulation.Present two new chaotic systems, realize them by circuit simulation are the main innovative points of this paper. It enriches the research contents of chaos and endues them the physical meanings. Moreover, the method of adaptive synchronization and fuzzy synchronization in this paper is effective and robust, they lay the foundation for their engineering applications.