INFLUENCE OF A SMALL PERTURBATION ON LOSS PULLING STABILITY OF SOLUTIONS TO SINGULARLY PERTURBATE EQUATIONS

Abstract

The paper considers the study of the solution of singularly perturbed differential equations. With the help of a specific example, the influence of a small perturbation on the delay in the loss of stability of solutions is shown. If a small perturbation is identically equal to zero, then in the space of real numbers one can choose the starting point so that the delay in the loss of stability is sufficiently large. The starting point is chosen in a stable interval. If a small perturbation is different from zero, then it will be necessary to pass to the complex region. In this case, the location of the level line in the complex plane does not capture the real axis. More precisely, there is no area in which the solution of the problem is investigated. Then there remains the possibility of delaying the loss of stability from the initial point to the zero point.