Related papers: A Linear Programming Approach to Dynamical Equival…
Mass-action kinetics is frequently used in systems biology to model the behaviour of interacting chemical species. Many important dynamical properties are known to hold for such systems if they are weakly reversible and have a low…
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…
A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and…
The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with a deficiency of at most one and exactly one terminal strong…
Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…
A reaction network together with a choice of rate constants uniquely gives rise to a system of differential equations, according to the law of mass-action kinetics. On the other hand, different networks can generate the same dynamical…
The Deficiency-One Theorem states that there exists a unique positive steady state in each positive stoichiometric class for weakly reversible deficiency-one mass action systems with one linkage class (regardless of the values of the rate…
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective…
It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be derived by considering the corresponding properties of a related generalized mass action…
Reaction networks can display a wide array of dynamics. However, it is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical equivalence and makes network identification a hard problem to…
In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often…
Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability…
Whereas the positive equilibrium of a mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples,…
Given a dynamical system with polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some network properties may guarantee specific dynamical properties,…
This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics. The original problem…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically…