The climate is a nonlinear dynamical system driven by the spatially inhomogeneous energy received from the Sun. The redistribution of energy involves a multitude of processes acting at various spatial and temporal scales. These processes are interconnected, leading to the existence of a multitude of feedback loops that can amplify or compensate each other until a steady state is reached, when a balance between the input of energy, dissipation and feedbacks occurs. Because of the presence of several feedbacks, there are different ways for these mechanisms to equilibrate. Thus, in general, there is not a unique resulting steady state under the same forcing, and the final state depends on the initial conditions, a situation referred to as ‘multistability’.

The study of alternative steady states is relevant for deep-time climate modelling, where large uncertainties exist on forcing, boundary, and initial conditions. The Permian-Triassic boundary (ca. 252 Ma) is a period marked by a huge magmatic activity in the Siberian Traps and one of the largest mass extinction, followed by oscillations in climatic conditions during the Early Triassic. The sequence of events that led to the mass extinction of marine and terrestrial species, as well as changes in vegetation distribution and the subsequent variations in the climate, are still unclear.

This thesis considers methods and concepts derived from the theory of dynamical systems to construct a numerical procedure which is well adapted to the study of deep-time climates. The multistability framework is used in the case of the Permian-Triassic paleogeography, by performing climate simulations with the MIT (Massachusetts Institute of Technology) general circulation model in a coupled atmosphere-ocean-sea ice-land configuration.

Results show the relevance of the multistability framework in the study of deep-time climates. The steady states that we obtain for the Permian-Triassic paleogeography open the possibility of interpreting climate oscillations in the geological records as tipping between one state and another. This has rich consequences which can be further explored with an interdisciplinary approach.