Analysis of the earth's carbon cycle models using biochemical systems theory and chemical reaction network theory

Date of Publication


Document Type


Degree Name

Doctor of Philosophy in Mathematics

Subject Categories



College of Science


Mathematics and Statistics Department

Thesis Adviser

Angelyn R. Lao

Defense Panel Chair

Glenn V. Alea


The global carbon cycle is a system which accounts for the different pools where carbon is stored (land, atmosphere, ocean and geological stock) and the processes that transfer carbon mass from one pool to another. Since this system is believed to be crucial in controlling the Earth's climate via regulation of the concentration of carbon dioxide (CO2) in the atmosphere, various mathematical models have been developed in order to better understand the system. This thesis proposes to examine global carbon cycle models using a combination of two approaches ¡ Biochemical Systems Theory (BST) and Chemical Reaction Network Theory (CRNT). BST is a canonical modelling framework based on power-law formalism on the other hand, CRNT is an approach that draws conclusions about the dynamical behaviour of a chemical reaction network (CRN) using the graphical structure of the network alone. The aim of the BST-CRNT analysis in this context is to learn the dynamical behaviour of a global carbon cycle model through a dynamically equivalent chemical kinetic system for the model. A chemical kinetic system is obtained by generating an appropriate CRN for a given model while its dynamical system is transformed into a BST system where each rate of carbon mass transfer is approximated with a power-law function. Three existing carbon cycle box models from literature were collected and analyzed using the proposed method. This thesis shows that the BST-CRNT analysis enhances our understanding of the capacity of the global carbon cycle system to reach a steady state, which is a natural starting point for assessing the systems potential to reach a stable equilibrium for which humans can safely operate (i.e. the desired state of the Earth). Furthermore, the method has also generated new results in the mathematical theory of power-law kinetic systems, which may be applicable in the analysis of other biological systems. One result involves a theorem (called Deficiency Zero Theorem) that characterizes the steady states of power-law kinetic systems with a special network decomposition. Another result centers around an algorithm (called Deficiency-One Algorithm) that decides for the capacity of a class of power-law kinetic systems to permit multiple steady states.

Abstract Format






Accession Number


Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

1 computer disc; 4 3/4 in.


Carbon cycle (Biogeochemistry); Chemical reactions

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