Eur. Phys. J. B (2014) 87: 227
https://doi.org/10.1140/epjb/e2014-50208-0

Regular Article

Regular and chaotic regimes in Saltzman model of glacial climate dynamics under the influence of additive and parametric noise

¹ Department of Mathematical Physics, Ural Federal University, Lenina ave., 51, 620000 Ekaterinburg, Russia
² School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK

^a e-mail: lev.ryashko@urfu.ru

Received: 26 March 2014
Received in final form: 18 April 2014
Published online: 7 October 2014

Abstract

It is well-known that the climate system, due to its nonlinearity, can be sensitive to stochastic forcing. New types of dynamical regimes caused by the noise-induced transitions are revealed on the basis of the classical climate model previously developed by Saltzman with co-authors and Nicolis. A complete parametric classification of dynamical regimes of this deterministic model is carried out. On the basis of this analysis, the influence of additive and parametric noises is studied. For weak noise, the climate system is localized nearby deterministic attractors. A mixture of the small and large amplitude oscillations caused by noise-induced transitions between equilibria and cycle attraction basins arise with increasing the noise intensity. The portion of large amplitude oscillations is estimated too. The parametric noise introduced in two system parameters demonstrates quite different system dynamics. Namely, the noise introduced in one system parameter increases its dispersion whereas in the other one leads to the stabilization of the climatic system near its unstable equilibrium with transitions from order to chaos.