Applying the Lotka–Volterra Model to the Dynamics of Chemical Reaction Networks

Overview

A distinguishing feature of complex systems is the non-linear dynamics relating microstates within a system’s phase space. At thermodynamic equilibrium, the probability of a system occupying a particular state may be derived from its partition function. However, for complex systems continuously driven from equilibrium by an external, low-entropy force, it is unlikely the system settles into a definite probability distribution. Their trajectory through phase space approaches a dynamical attractor, which is modeled with differential equations rather than statistical ensembles. The complex systems explored in this paper are chemical reaction networks, in which the relative frequency of each chemical species is determined by the current frequencies of the others. We investigate an alternative method to representing this behavior based on the Lotka–Volterra equations used in ecology to model population. Living species are replaced with chemical species, and environmental competition is replaced with competition between parallel chemical processes for common reagents. We show this model’s connection to the partition function, illustrating entropy’s role in both representations. Lastly, we apply this novel method to chemical networks independently analyzed using traditional methods of kinematics, and compare the results. In particular, we consider systems with unusual fine-tuning to their environment, such that they occupy a low-entropy state whose dissipation of free energy is exceptionally greater than a more typical high-entropy configuration. These low-entropy systems avoid settling into static equilibria so long as there is a source of free energy, and enable analysis of the physics governing the emergence of self-sustaining processes found in biology.

Competition history

• AJAS 2019 Category not listed

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