Complex balanced equilibria of weakly reversible poly-PL systems: existence, stability, and robustness

TL;DR

This paper investigates the existence, stability, and robustness of complex balanced equilibria in weakly reversible poly-PL systems, extending known results for generalized mass action systems through new representations and transformations.

Contribution

It introduces a canonical power law form and a transformation method for poly-PL systems, enabling analysis of their dynamical properties and robustness features.

Findings

Existence and uniqueness of complex balanced steady states established.

Linear stability of complex balanced equilibria demonstrated.

Identification of concentration robustness in certain species.

Abstract

Poly-PL kinetic systems (PYK) are kinetic systems consisting of nonnegative linear combinations of power law functions. In this contribution, we analyze these kinetic systems using two main approaches: (1) we define a canonical power law representation of a poly-PL system, and (2) we transform a poly-PL system into a dynamically equivalent power law kinetic system that preserves the stoichiometric subspace of the system. These approaches led us to establish results that concern important dynamical properties of poly-PL systems that extend known results for generalized mass actions systems (GMAS) such as existence, uniqueness and parametrization of complex balanced steady states, and linear stability of complex balanced equilibria. Furthermore, the paper discusses subsets of poly-PL systems that exhibit two types of concentration robustness in some species namely absolute concentration robustness and balanced concentration robustness.