Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane

Abstract

When studying any dynamical system the critical values of its parameters are of special interest. Properties of stationary or quasistationary regimes change fundamentally, i.e. the bifurcation is observed. One type of bifurcation, when asymptotic stability condition is disturbed and limiting process is carried out, appears in the systems occurring in laser physics, chemical kinetics, plastic deformation, biophysics, in the modified Ziegler system, and when modeling the crown forest fire and safe combustion with maximum temperature. Using the stationary phase method the author has constructed the asymptotic for solving singularly perturbed ordinary differential equations with periodic turning points in the complex plane when the condition of asymptotic stability is disturbed. The obtained asymptotic estimation for solving the problem is not the improved one.

Keywords

• solution asymptotic
• turning point
• singularly perturbation
• asymptotic stability
• Stokes line
• ordinary differential equation