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 nonlinear models is perturbation methods. I show that, as typically implemented, these methods are incapable of finding solutions featuring limit cycles or chaos. Fundamentally, solutions are only required not to explode, while standard perturbation algorithms seek solutions that meet the stronger requirement of convergence to the steady state. I propose a modification to standard algorithms that does not impose this overly strong requirement.

中文翻译：

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鞍形循环：使用扰动方法求解具有极限循环（或混沌）特征的理性预期模型

与线性模型不同，非线性商业周期模型即使在没有冲击的情况下也能产生持续的波动（例如，通过极限周期/混沌）。解决非线性模型的一种流行方法是扰动方法。我表明，按照通常实施的方式，这些方法无法找到具有极限环或混沌特征的解决方案。从根本上说，解决方案只要求不爆炸，而标准扰动算法寻求满足收敛到稳态的更强要求的解决方案。我建议对标准算法进行修改，但不会强加这种过于强烈的要求。