We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence ...We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.展开更多
The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of ...The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of the problem. At the same time, Based on sewing techniques, the existence of the smooth impulsive solution and the uniform validity of the asymptotic expansion are proved.展开更多
基金Supported by the National Natural Science Foundation of China(No.71501130)Natural Science Foundation of Hebei Province(A2015407063)
文摘We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.
基金Supported by the National Natural Science Foundation of China (No. 11071075, 11171113)the NNFC-the Knowledge Innovation Program of Chinese Academy of Science (No. 30921064, 90820307)E-Institutes of Shanghai Municipal Education Commission (No. E03004)
基金Supported by the National Natural Science Foundation of China(N.11501236,N.11471118,N.30921064 and 90820307),the Innovation Project in the Chinese AcademDepartment of Mathematics,Shanghai Key Laboratory of PMMP,East China Normal University
文摘The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of the problem. At the same time, Based on sewing techniques, the existence of the smooth impulsive solution and the uniform validity of the asymptotic expansion are proved.
