The stability of interval two-dimensional semi-linear differential equations based on constrained interval arithmetic

Abstract

In this study, the constrained interval arithmetic (CIA) is used as an effective mathematical tool for solving the stability analysis for interval two-dimensional semi-linear differential equations. Under certain assumptions, the origin is a focus of the interval semi-linear differential equations if it is a focus of the interval linear ones. Meanwhile, the origin can be a center, a center-focus or a focus of interval semi-linear differential equations if it is a center of the interval linear ones. On the other word, the types of equilibrium point are still determined by the linear part when a nonlinear disturbance is added to the interval linear differential equations. Based on CIA, the stability results of interval differential equations are the same as those of the real differential equations. At last, three illustrative examples validate the stability results of the origin for interval two-dimensional semi-linear differential equations.