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

We consider the scalar delay differential equation (x) over dot(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 Kchanges. The generated periodic orbits are of large amplitude in the sense that they oscillate about both unstable fixed points of f(K). (c) 2020 Elsevier Inc. All rights reserved.