On the Local Dynamics of an Equation with Two Large Proportional Delays

Investigations of the local dynamics of singularly perturbed equations with two delays are carried out for the casein which both the delays are asymptotically large and, at the same time, of the same order (proportional). Critical cases were identified, and it was shown that all of them have infinite dimension. To study the behavior of solutions in cases close to critical, special nonlinear equations (quasinormal forms) were constructed whose solutions provide asymptotic approximations of the solutions to the original problem.