Nonlinear Analysis Of Chaotic Circuit

Real system mostly contain nonlinear factors, the traditional linear theory has far can’tadapt to the needs of the development of modern society, with the rapid development ofmodern industry, its dynamics behavior is becoming more and more complex, withlinearization theory cannot explain the various dynamics of chaos phenomenon. Therefore,nonlinear theory is due to demand, and achieved rapid development. Based on chua’s circuit,on the basis of system dynamics behavior research, further study on the basic concepts anddefinitions of fractional order chua’s circuit and its dynamic behavior, at the same time toconsider a new three-dimensional autonomous systems under random factors of nonlinearphenomena, on the basis of system design and a new three-dimensional autonomous chaoticsystem are numerically simulated.Chua’s circuit is one of the common nonlinear systems, for integer order systemdynamics behavior research, the domestic and foreign scholars have done a lot of work, andmany important conclusions are obtained. In real life, however, the main there is a non integerorder. Therefore, study the dynamic behavior of fractional order chaotic systems has is a keypoint in the nonlinear field of research direction. In this paper, the tsai and fractional orderchua’s circuits system under random factors of the dynamic behavior of the numericalsimulation of the main contents are as follows:First chapter is introduction, mainly introduced the current development of nonlineardynamic system and the research purpose and significance of the fractional order chua’scircuit system, and the structure in this paper, the main work and made a simple description.The second chapter the basic theory of fractional order calculus, mainly introduces thebasic concept of fractional order calculus, mathematical definition, and research on basictheory of chaos and chua’s circuit used in system dynamics behavior basic method has madethe simple introduction.Chapter3random factors under elastic collision vibration syste m dynamic behavioranalysis, first of all random factors affect collision single degree of freedom vibration systemis used to numerically simulate, analyze its dynamic behavior; Next to the collision of twosingle degree of freedom vibration system under random factors influence carries on thenumerical simulation and analysis of the dynamic behavior of the model; Finally collision ofdouble degree of freedom vibration system in dynamic behavior under the influence ofrandom factors was analyzed, and combined with the system of the bifurcation diagram,phase diagram, time response diagram and poincare section falls figure, summed up therandom factors on the elastic collision vibration system dynamic behavior. Chapter4random factors under a new three-dimensional autonomous system dynamicsanalysis, mainly based on the system design of a new three-dimensional autonomous chaoticsystem and numerical simulation, finally has made the system of the bifurcation diagram,phase diagram and time response diagram, draw relevant conclusions.