Nonsmooth Homoclinic Bifurcation in a Conceptual Climate Model

TL;DR

This paper investigates a unique nonsmooth homoclinic bifurcation in a climate model, revealing how boundary collisions and virtual equilibria lead to complex global bifurcation phenomena.

Contribution

It introduces the concept of nonsmooth homoclinic bifurcation in a climate context and analyzes its relation to smooth bifurcation structures.

Findings

Identification of nonsmooth homoclinic bifurcation in a climate model

Relation between boundary collisions and global bifurcations

Comparison of nonsmooth and smooth bifurcation structures

Abstract

Collision of equilibria with a splitting manifold has been locally studied, but might also be a contributing factor to global bifurcations. In particular a boundary collision can be coincident with collision of a virtual equilibrium with a periodic orbit, giving an analogue to a homoclinic bifurcation. This type of bifurcation is demonstrated in a nonsmooth climate application. Here we describe the nonsmooth bifurcation structure, as well as the smooth bifurcation structure for which the nonsmooth homoclinic bifurcation is a limiting case.