Dynamics Of Genaral Rossler System And Jerky Equation

In this thesis,by bifurcation theory and numerical simulations,we focus on the dy-namic behaviors of two typically nonlinear dynamical systems.First,the general Rossler system is discussed.It is proved that this system undergoes fold bifurcation,Hopf bifur-cation,fold-Hopf bifurcation and Bogdanov-Takens bifurcation.In addition,the direction of the Hopf bifurcation and the stability of the limit cycle are also judged.Moreover,numerical simulations using AUTO and MATLAB,including bifurcation diagrams,phase portraits,are presented to further verify theoretical results.It is found that the Hopf bifur-cation point can be supercritical,subcritical,or degenerate and the number of degenerate Hopf bifurcation is different with different bifurcation parameters.Following,the general jerky equation is discussed.It also undergoes fold bifurcation,Hopf bifurcation,fold-Hopf bifurcation and Bogdanov-Takens bifurcation.Numerical simulations including the fold bifurcation of limit cycles are presented.