Saddle cycles: Solving rational expectations models featuring limit cycles (or chaos) using perturbation methods

Unlike linear ones, nonlinear business cycle models can generate sustained fluctuations even in the absence of shocks (e.g., via limit cycles/chaos). A popular approach to solving is perturbation methods. I show that, as typically implemented, these methods are incapable finding solutions featuring cycles or chaos. Fundamentally, only required not explode, while standard algorithms seek that meet stronger requirement convergence steady state. propose a modification does impose this overly strong requirement.