Asymptotics of Andronov–Hopf Dynamic Bifurcations

We consider a system of two nonlinear differential equations with slowly varying parameter μ = εt. For frozen const the has focus type equilibrium state stability which changes when passing through value 0, i.e., we deal an Andronov–Hopf bifurcation. Using normal form method combined averaging method, study asymptotics respect to small ε → 0 for solutions having narrow transient layer near bifurcation point in domain |εt| ≪ 1. express leading term terms solution Bernoulli equation.