Damped Perturbations of Systems with Center-Saddle Bifurcation

An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence time damped perturbations power-law asymptotics investigated. particular solutions tending at infinity to fixed points limiting are stability these analyzed when parameter unperturbed takes critical and non-critical values. Conditions that ensure persistence perturbed described. When broken, pair degenerate point appears case. It shown that, depending on structure parameters perturbations, one can be stable, metastable or unstable, while other solution always unstable.