Document Type

Article

Publication Date

1994

DOI

10.5194/npg-1-31-1994

Publication Title

Nonlinear Processes in Geophysics

Volume

1

Issue

1

Pages

31-40

Abstract

A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet. We apply standard perturbative techniques from dynamical systems theory to study small amplitude periodic orbits about a constant equilibrium. The equations are put in cononical form and the local phase space topology is examined. Maximum and minimum periods of oscillation are obtained and related to the radius of the orbit. An adjacent equilibrium is shown to have saddle character and the inflowing and outflowing manifolds of this saddle are studied using numerical integration. The inflowing manifolds show the region of attraction for the periodic orbit. As the frequency gets small, the adjacent (saddle) equilibrium approaches the radius of the periodic orbit. The bifurcation of the periodic orbit to a stable homoclinic orbit is observed when an inflowing manifold and an outflowing manifold of the adjacent equilibrium cross.

Comments

Web of Science: "Free full-text from publisher." © European Geophysical Society 1994.

Original Publication Citation

Toner, M., & Kirwan, A. D. (1994). Periodic and homoclinic orbits in a toy climate model. Nonlinear Processes in Geophysics, 1(1), 31-40. doi:10.5194/npg-1-31-1994

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