A Class Of Nonlinear Differential Equations, Bifurcation And Chaos Study

In this dissertation, the nonlinear gas discharge equations are solved by computational simulation and the nonlinear behavior, such as bifurcation and chaos, are discussed according to the simulation results. The gas discharge equations are obtained from the physical laws and by introducing the new scales, the gas discharge equations can be simplified used the dimensionless variables and an analytical approximations of the equations have been derived based on the central manifold theory. The equations are reduced to the fairly simple forms by the adiabatic elimination of electrons. In the third chapter, the algorithm for the gas discharge equations are studied in detail, and the whole computational scheme is presented. At the last chapter, the computational results are investigated guiding by the theory of the dynamic system, introduced in the first chapter. The supercritical Hopf bifurcation is observed due to the increase of the applied voltage or the value of the semiconductor conductance. The strange attractor appears as the applied voltage reaches the certain value and the Lyapunov spectrum shows the system transits into the chaotic state. The quasiperiodicity to chaos is also referred in this dissertation.