Related papers: Structural conditions for saddle-node bifurcations…
In this paper, we propose a new method to identify biochemical reaction networks (i.e. both reactions and kinetic parameters) from heterogeneous datasets. Such datasets can contain (a) data from several replicates of an experiment performed…
We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for the following stability condition to hold: each state in a closed, irreducible component of the state space is positive…
We establish that mass conserving single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This result holds for closed systems without…
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the…
We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to…
Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective…
We study the multistationarity for the reaction networks with one-dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states. We prove that if a network admits multistationarity, then…
A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…
Various biological phenomena, like cell differentiation and pattern formation in multicellular organisms, are explained using the bifurcation theory. Molecular network motifs like positive feedback and mutual repressor exhibit bifurcation…
In chemical reactions, trajectories typically turn from reactants to products when crossing a dividing surface close to the normally hyperbolic invariant manifold (NHIM) given by the intersection of the stable and unstable manifolds of a…
Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize…
We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows…
We present a computational procedure to characterize the signs of sensitivities of steady states to parameter perturbations in chemical reaction networks.
In this paper we investigate pattern formation in Keller--Segel chemotaxis models over a multi--dimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its…
The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system…
Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and…