Related papers: First order endotactic reaction networks
The fundamental decomposition of a chemical reaction network (also called its "$\mathscr{F}$-decomposition") is the set of subnetworks generated by the partition of its set of reactions into the "fundamental classes" introduced by Ji and…
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…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
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…
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
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…
Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence,…
A reaction system exhibits "absolute concentration robustness" (ACR) in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this means that the positive part of the variety…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
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…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
We study the limiting behavior of a random dynamic system driven by a stochastic chain. Our main interest is in the chains that are not necessarily ergodic but rather decomposable into ergodic classes. To investigate the conditions under…
We present a model for the evolution of networks of occupied sites on undirected regular graphs. At every iteration step in a parallel update I randomly chosen empty sites are occupied and occupied sites having degree outside of a given…
Maintaining stability in an uncertain environment is essential for proper functioning of living systems. Robust perfect adaptation (RPA) is a property of a system that generates an output at a fixed level even after fluctuations in input…
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…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…