Related papers: A network dynamics approach to chemical reaction n…
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…
In this paper we derive a compact mathematical formulation describing the dynamics of chemical reaction networks that are complex-balanced and are governed by mass action kinetics. The formulation is based on the graph of (substrate and…
The characterization of the notions of complex and detailed balancing for mass action kinetics chemical reaction networks is revisited from the perspective of algebraic graph theory, in particular Kirchhoff's Matrix Tree theorem for…
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…
Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that…
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…
The study of the dynamics of chemical reactions, and in particular phenomena such as oscillating reactions, has led to the recognition that many dynamical properties of a chemical reaction can be predicted from graph theoretical properties…
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological,…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the…
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…
Dynamical systems arising from chemical reaction networks with mass action kinetics are the subject of chemical reaction network theory (CRNT). In particular, this theory provides statements about uniqueness, existence, and stability of…
In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies…
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…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we…
Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…