Dynamical Study And Circuit Simulation Of New Chaotic Systems

The design of chaotic circuit and its application in chaotic secret communication have been a recent pursuit in the fields of nonlinear circuit and system. It originates not only from the impressive discovery of chaotic attractor by Lorenz back in 1960s, but also from the Chua's circuit proposed by Chua shaotang in 1980s. Recently, increasingly importance has been attached to the discovery of new chaotic systems and chaotic circuit realization.A new chaotic system is proposed in this paper. It is a three-dimensional autonomous system with four real variables, three variables and only two quadratic terms. The new system can generate highly symmetrical double-wing attractor. Some dynamical properties of this new system, such as the stability of the fixed points, sensitivity of system, Lyapunov Exponent analysis, fractal dimension, Poincarémap are studied and the chaotic numerical simulation results are verified. Moreover, the evolution of the new chaotic system is studied according to the variation of four real variables, the results show that the new chaotic system can exhibit complex chaotic dynamics. A linear real variable is introduced to the new chaotic system to control the wing shape of its attractor according to the variation of the linear real variable.Especially, the circuit realization of the new chaotic system is presented in this paper, and its new circuit structure has been studied. Chaotic circuit is consisted of operational amplifiers, mutipliers along with some basic linear resistances and capacities. The oscillator circuit of this chaotic dynamical system has been designed and simulated based on Electronics Workbench (EWB). The chaotic electronical attractors and the time domain waveforms of three chaotic singals are generated and showed on oscilloscope. The simulation results are correct and have been verified.Furthermore, a 4-D autonomous chaotic system is presented in this paper, which is also called hyperchaotic system. The phase portraits, chaotic singals' time domain waveforms of the chaotic system are presented, and the sensitivity of system is studied. The chaotic circuit has been designed relevent to the new 4-D chaotic system based on EWB, and its simulation has been carried out. The chaotic electronical attractors and the time domain waveforms of four chaotic singals are generated and showed on oscilloscope. The simulation results are correct and have been verified.