MULTISTATIONARITY IN EARTH’S PRE-INDUSTRIAL CARBON CYCLE MODELS
N.T. Fortun, A.R. Lao, L.F. Razon, and E.R. Mendoza (pp. 81-96)
Abstract
Chemical reaction networks (CRNs) provide a language for representing systems of interacting entities. In this paper, the pre-industrial carbon cycle models of Schmitz (2002) and Anderies et al. (2013) are viewed and analyzed as CRNs. In this framework, we assess the models’ capacity for multiple steady states or multistationarity via Chemical Reaction Network Theory – an approach that associates the topological structure of the CRN to the dynamical behavior of the network. Using the computational approach of Feliu & Wiuf (2013), this paper shows that the CRN representation of the pre-industrial model of Schmitz is injective, which is sufficient to conclude that the system cannot admit multiple steady states. On the other hand, the multistationarity of the pre-industrial model of Anderies et al. is shown using the criterion for the uniqueness of complex balancing equilibrium of Müller & Regensburger (2012).