Stability And Bifurcation Of Two Kinds Of Nonlinear Models

In this paper,the problems of the stability and bifurcation for aeroelastic system and the limit cycles and local critical periods for piecewise smooth systems are mainly studied,there are four chapters as follows.Chapter one,the progress and research status of the above two kinds of problems are discussed,and the specific contents of each chapter are introducedChapter two,the stability and bifurcation at the degenerate equilibrium point of a class of two-dimensional airfoil aeroelastic systems are discussed.The numerical simulation is used to verify the rationality of the theoretical analysis.Chapter three,the problems of limit cycles and local bifurcations of critical periods of a class of quartic Riccati switching systems are studied.it is proved that the system has at most 10 limit cycles in the neighborhood of the origin,under the three central conditions,the number of the local critical periods from the origin are 6,3 and 7 separately.Chapter four,the whole work of the thesis is summarized and the prospects of the future are given.