Related papers: The inheritance of local bifurcations in mass acti…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
Any mass action network gives rise to a parameterised family of polynomial equations whose positive solutions are the positive equilibria of the network. Here, we consider alternative systems of equations, whose solutions are in smooth,…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
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…
In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic…
A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…
Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space…
A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following…
This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems…
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…
This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of Chemical Reaction…
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition…
Motivated by investigating multistationarity in biochemical systems, we address saddle-node bifurcations for chemical reaction networks endowed with general kinetics. At positive equilibria, we identify structural network conditions that…
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…
We address several questions in reduced versus extended networks via the elimination or addition of intermediate complexes in the framework of chemical reaction networks with mass-action kinetics. We clarify and extend advances in the…
The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a polynomial differential equation, is it possible…
We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE) and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction networks (CRNs). Specifically, when is it that we can…
In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…