Guzsvány Szandra: Saddle-Node-Like Bifurcation of Periodic Orbits for a Delay Differential Equation

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 $f$.