Perturbation of a Nonsmooth Supercritical Hopf Bifurcation

Abstract

Nonsmooth formulations of physical models are common, particularly in climate modeling. However, in many of these models, there is little justification for this modeling choice, and no mathematical indication that the resulting behavior in the nonsmooth system is consistent with behavior that would arise in a similar smooth system. I explore this question by analyzing the relationship between a smooth and nonsmooth Hopf bifurcation in one particular climate example. I show that the nonsmooth bifurcation perturbs to the smooth bifurcation under small changes in a limiting parameter.

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• Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system
• Nonlinear threshold behavior during the loss of Arctic sea ice
• Non-determinism in the limit of nonsmooth dynamics
• Regularizations of two-fold bifurcations in planar piecewise smooth systems using blow up