Asymptotics of Dynamical Saddle-node Bifurcations
Received 14 December 2020; accepted 18 February 2022
2022, Vol. 18, no. 1, pp. 119-135
Author(s): Kalyakin L. A.
Dynamical bifurcations occur in one-parameter families of dynamical systems, when the
parameter is slow time. In this paper we consider a system of two nonlinear differential equations
with slowly varying right-hand sides. We study the dynamical saddle-node bifurcations that occur
at a critical instant. In a neighborhood of this instant the solution has a narrow transition layer,
which looks like a smooth jump from one equilibrium to another. The main result is asymptotics
for a solution with respect to the small parameter in the transition layer. The asymptotics is
constructed by the matching method with three time scales. The matching of the asymptotics
allows us to find the delay of the loss of stability near the critical instant.
Download File PDF, 346.24 Kb |
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License