Limit Cycle Problem Of A Piecewise Linear Dynamic Syste

In this thesis,we study the dynamics of two piecewise linear systems:The first system is a continuous planar piecewise linear system with two degenerate subsystems and three zones separated by two parallel lines.We prove that the system has at most two limit cycles,give the bifurcation diagram and global topological phase portraits of the system of DDF and DDC cases,and find the system has the boundary equilibria bifurcation,the grazing bifurcation for limit cycles,the double limit cycle bifurcation,three new scabbard bifurcations,and two new Poincare-like bifurcations.The second system is a discontinuous planar piecewise linear system of FC and CC cases with two regions separated by a straight line.We prove that the system has at most two limit cycles,give the bifurcation diagram of the system for a particular condition,and find three new Hopf bifurcations.Finally,we give the global topological phase portraits of the system.For the first system,the method we adopt is to compute the integrals of the divergence.For the second system,the method we adopt is the point transformation method.