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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…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable. We study the asymptotic stability of ac-networks --- robust heteroclinic networks that exist in smooth ${\mathbb…
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…
Informally, a chemical reaction network is "atomic" if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational…
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…
Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…
Living systems operate out of equilibrium, continuously consuming energy to sustain organised, functional states. Their emergent behaviour usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainment and…
Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where…
A complex balanced kinetic system is absolutely complex balanced (ACB) if every positive equilibrium is complex balanced. Two results on absolute complex balancing were foundational for modern chemical reaction network theory (CRNT): in…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete…
The concept of limiting step gives the limit simplification: the whole network behaves as a single step. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles…
Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…
Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at…
This paper presents new results about the optimization based generation of chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown that the graph structure of the realization containing the maximal number of reactions…
Inspired by Anderson et al. [J. R. Soc. Interface, 2014] we study the long-term behavior of discrete chemical reaction networks (CRNs). In particular, using techniques from both Petri net theory and CRN theory, we provide a powerful…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…