Related papers: Multistability of small zero-one reaction networks
The distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice paper of Wang and…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
We present herein an extension of an algebraic statistical method for inferring biochemical reaction networks from experimental data, proposed recently in [3]. This extension allows us to analyze reaction networks that are not necessarily…
Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…
External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…
We show that weakly reversible mass-action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible…
Delays are an important phenomenon arising in a wide variety of real world systems. They occur in biological models because of diffusion effects or as simplifying modeling elements. We propose here to consider delayed stochastic reaction…
In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
The problem of achieving consensus in a network of connected systems arises in many science and engineering applications. In contrast to previous works, we focus on the system reactivity, i.e., the initial amplification of the norm of the…
We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First,…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
Multistationarity is the property of a system to exhibit two distinct equilibria (steady-states) under otherwise identical conditions, and it is a phenomenon of recognized importance for biochemical systems. Multistationarity may appear in…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
An important invariant of a chemical reaction network is its maximum number of positive steady states. This number, however, is in general difficult to compute. Nonetheless, there is an upper bound on this number -- namely, a network's…
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…
This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a…
Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here for homogeneous networks, by showing that every homogeneous…
Molecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signalling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory…