论文标题
具有中心垫分叉的系统的阻尼扰动
Damped perturbations of systems with centre-saddle bifurcation
论文作者
论文摘要
考虑到具有中心垫分叉的平面中普通微分方程的自主系统。研究了时间引起幂律渐近药的扰动的影响。考虑了限制系统固定点的特定解决方案。当不受干扰的系统的分叉参数具有关键和非关键值时，分析了这些解决方案的稳定性。描述了确保扰动系统中分叉持续性的条件。当分叉破裂时，在关键情况下会出现一对倾向于限制系统退化固定点的溶液。结果表明，根据扰动的结构和参数，这些解决方案之一可以是稳定，可稳定或不稳定的，而另一种解决方案始终是不稳定的。
An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence of time damped perturbations with power-law asymptotics is investigated. The particular solutions tending at infinity to the fixed points of the limiting system are considered. The stability of these solutions is analyzed when the bifurcation parameter of the unperturbed system takes critical and non-critical values. Conditions that ensure the persistence of the bifurcation in the perturbed system are described. When the bifurcation is broken, a pair of solutions tending to a degenerate fixed point of the limiting system appears in the critical case. It is shown that, depending on the structure and the parameters of the perturbations, one of these solutions can be stable, metastable or unstable, while the other solution is always unstable.
