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Non-smooth homoclinic bifurcation in a conceptual climate model

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… Click to show full 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 non-smooth climate application. Here, we describe the non-smooth bifurcation structure, as well as the smooth bifurcation structure for which the non-smooth homoclinic bifurcation is a limiting case.

Keywords: bifurcation conceptual; climate; non smooth; homoclinic bifurcation; smooth homoclinic; bifurcation

Journal Title: European Journal of Applied Mathematics
Year Published: 2018

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