Guzsvány Szandra
(Szegedi Tudományegyetem, Bolyai Intézet)

Saddle-node-like bifurcation of periodic orbits for a delay differential equation

Absztrakt: We consider the scalar delay differential equation x'(t) = -x(t) + f(x(t-1)) with a nondecreasing feedback function f depending on a parameter K, and we verify that a saddle-node-like bifurcation of periodic orbits takes place as K varies. The nonlinearity f 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.