DELAYING THE LOSS OF STABILITY SOLUTION OF SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS

Abstract

The paper considers the study of the solution of singularly perturbed differential equations. In the course of the study, the priority is to choose the largest possible interval. The starting point is chosen in a stable interval. The equation does not contain a term that has a small perturbation. When moving to the complex area, a level line appears. The expansion of the responsiveness of solutions depends on the location of the level line. Therefore, a nonlinear differential equation is considered and the study is carried out in the space of real numbers. The research is based on a specifically chosen function and the theorem is proved. The considered interval captures the points of change of stability.