Saddle-Node Bifurcation of Periodic Orbits for a Delay Differential Equation

2018/10/27 by Guzsvány, Szandra, Vas, Gabriella
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.11679

Abstract

We consider the scalar delay differential equation x(t)=-x(t)+f_K(x(t-1)) with a nondecreasing feedback function f_K depending on a parameter K, and we verify that a saddle-node bifurcation of periodic orbits takes place as K varies. The nonlinearity f_K is chosen so that it has two unstable fixed points (hence the dynamical system has two unstable equilibria), and these fixed points remain bounded away from each other as K changes. The generated periodic orbits are of large amplitude in the sense that they oscillate about both unstable fixed points of f_K.

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