Periodic Orbits for a Discontinuous Vector Field Arising from a Conceptual Model of Glacial Cycles

TL;DR

This paper analyzes a conceptual climate model with a discontinuous vector field, demonstrating the existence of a large periodic orbit that models intrinsic glacial cycles, including alternating glaciations and deglaciations.

Contribution

It introduces a novel discontinuous dynamical system model for glacial cycles and proves the existence of a large periodic orbit crossing the discontinuity boundary.

Findings

Existence of a large periodic orbit in the model

Orbit crosses the discontinuity boundary, representing climate transitions

Model captures intrinsic glacial cycle dynamics

Abstract

Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems. Here we discuss a conceptual model of glacial cycles consisting of a system of three ordinary differential equations defining a discontinuous vector field. We show that this system has a large periodic orbit crossing the discontinuity boundary. This orbit can be interpreted as an intrinsic cycling of the Earth's climate giving rise to alternating glaciations and deglaciations.