相关论文: Stability conditions of chemical networks in a lin…

Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…

Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as networks, these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been…

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…

Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the…

A decomposition of a chemical reaction network (CRN) is produced by partitioning its set of reactions. The partition induces networks, called subnetworks, that are "smaller" than the given CRN which, at this point, can be called parent…

Reaction networks (RNs) comprise a set $X$ of species and a set $\mathscr{R}$ of reactions $Y\to Y'$, each converting a multiset of educts $Y\subseteq X$ into a multiset $Y'\subseteq X$ of products. RNs are equivalent to directed…

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 introduce the boundary reproduction number, adapted from the next generation matrix method, to assess whether an infusion of species will persist or become exhausted in a chemical reaction system. Our main contributions are as follows:…

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…

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,…

We analyze the coherent dynamics of excitons in three dimensional topologically disordered networks with traps. If the interactions between the nodes of the network are long ranged, i.e., algebraically decaying as a function of the distance…

Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their…

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…

We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…

Relaxation dynamics in reversible catalytic reaction networks is studied, revealing two salient behaviors that are reminiscent of glassy behavior: slow relaxation with log(time) dependence of the correlation function, and emergence of a few…

We show that very simple molecular systems, modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts…

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,…

In this paper mathematical models for the evolutionary conserved Notch-Delta pathway are developed and analyzed in order to better understand how two neighboring biological cells can become different. We pursue a structure-based…

Chemical and biological networks can describe a wide variety of processes, from gene regulatory networks to biochemical oscillations. Modeled by chemical master equations, these processes are inherently stochastic, as fluctuations dominate…

The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…