Dynamic Behavior And Bifurcation Analysis Of Nonlinear Circuit System

In recent years, with the rapid development of simulation technology, the circuit model is becoming more and more important in both academic research and in the actual engineering application. Therefore, the complex behavior of nonlinear circuit also becomes one of research hot topics in circuit system. The third-order and fourth-order Chua's circuit is the research object. The dynamics phenomena of systems were studied by analyzing a series of theory and numerical simulation with the differential contain knowledge and Routh- Hurwitz criterion.In the research of Third-order Chua's circuit system, its dynamics differential equation was given to analyze stability and bifurcation of balance point on each boundary surface. The mathematical model was converted into standard form of differential inclusion. The dynamic behavior of system on nonsmooth boundary was analyzed based on the generalized Jacobi matrix on the boundary surface. The parameters were derived of system bifurcation behavior happening. The simulation diagram was given with the method of numerical simulation. It showed that the third-order Chua's system lead to the chaos, and there was a periodic and quasi-periodic state of the entire system. And then the fourth-order Chua's circuit was analyzed, the stability and bifurcation of balance point of each area was carried on the detailed analysis by taking the same analysis method. The key point is the bifurcation of nonsmooth boundary surface. The mathematical model of the fourth-order Chua's circuit was converted into standard form of differential inclusion. The bifurcation on the boundary surface of the system was discussed by studying the eigenvalues curve of the generalized Jacques matrix. Several kinds of graphics were simulated on the basis of the numerical simulation method to analyze the system motion. It showed that the fourth-order chua's circuit system became the single vortex volume attractor from the stable state, and then formed double turbination attractor. The system leads to a state of chaos with rich movement characteristics from the clearly bifurcation diagram.