Most Probable Phase Portraits of Stochastic Differential Equations and its Numerical Simulation

A practical and accessible introduction to most probable phase portraits is given. The reader is assumed to be familiar with stochastic differential equations and Euler-Maruyama method in numerical simulation. The article first introduce the method to obtain most probable phase portraits and then give its numerical simulation which is based on Euler-Maruyama method. All of these are given by examples and easy to understand.