Periodic Solutions Of Several Pulsed Differential Equations And Their Branches

In this thesis, we will discuss the existence, stability and bifurcations of periodic solu-tions of a certain scalar impulsive differential equations on Moebius strip. Some sufficient conditions are obtained to ensure the existence and stability of one-side periodic orbit and two-side periodic orbit of impulsive differential equations on Moebius strip by employing displacement functions. Furthermore, double-periodic bifurcation is also studied by using Poincare map. In this paper, we will concern about the stability and bifurcation to a cer-tain kind of planar impulsive dynamical systems. The main tools used here are Poincare mapping and displacement functions. Meanwhile, it shows how the impulse effects influ-ence the structure of the trajectories on the phase plane.