带高阶转向点的一阶非线性奇摄动初值问题的鸭轨道

Canard Orbits in First-order Nonlinear Singularly Perturbed Initial Value Problems with a Higher-order Turning Point

基于一阶初值问题的微分不等式,通过构造所需动力学性质的上下解函数,研究带高阶转向点的一阶非线性奇摄动初值问题鸭轨道的存在性.通过一个典型例子,验证了理论结果的正确性;同时数值积分也证实了该理论结果.

Based on the differential inequalities of first-order initial value problems, by constructing the upper and lower solutions with desired dynamics, deals with the existence of canard orbits in first-order nonlinear singularly perturbed initial value problems with a high- er-order turning point. A typical example is performed to verify the correctness of the theo- retical results. Numerical integrations also demonstrate the theoretical results.