Canard轨迹原理

The principle of the phase track of Canard

为了精确的求出Canard轨迹的描述方程,提出了一个分段表达的非线性模型,能直接求出一个非线性二阶自治方程的相轨迹方程的解析解,能定量求出Canard轨迹的描述方程和参数条件,可以用两类方程简单描述所有的Canard轨迹.

The complex phase tracks of Canard have caused concern of the scientists in the fields of physics, biology and chemistry. In order to find the accurate function describing the phase track of Canard, a nonlinear model involving consecutive segments is suggested,from which the analytical solution of the phase track function of a nonlinear second order autonomous function can be readily obtained,therefore the function describing the phase track of a Canard and its parametric conditions can be obtained analytically. It follows that all the phase tracks can be simply described by two kinds of functions.