The principle of the phase track of Canard

Abstract

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.