Canard Of A Piecewise Smooth Singularly Perturbed System

In the thesis,canard of a singular perturbation system was analyzed,including the existence of the duck solution and estimation of the control parameter.For piecewise smooth system,I have found an appropriate smooth system,and give some the corresponding properties.In the paper,a smooth shadow system has been introduced.The trajectory of the piecewise smooth system is bounded by the trajectory of the shadow system.Furthermore,I have built the outer boundary line of the original system.With Poincare-Bendixson theorem,I get the existence of periodic trajectory in this piecewise smooth system.By analyzing the equilibrium point of the system,I get the duck solution of this piecewise smooth system.In order to estimate the control parameters of the singularly perturbed system,we give the regularization of the piecewise smooth system.The regularized equation is smooth in a small region.And I use the Blow-up method to analyze the duck solution in a neighborhood of origin for the regularized system,and then get the estimation of control parameter,so do the original piecewise smooth system.