Related papers: Homeostasis and injectivity: a reaction network pe…
We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with…
This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or…
Homeostasis is a running theme in biology. Often achieved through feedback regulation strategies, homeostasis allows living cells to control their internal environment as a means for surviving changing and unfavourable environments. While…
Correlation-based Hebbian plasticity is thought to shape neuronal connectivity during development and learning, whereas homeostatic plasticity would stabilize network activity. Here we investigate another, new aspect of this dichotomy: Can…
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…
Which reaction networks, when taken with mass-action kinetics, have the capacity for multiple steady states? There is no complete answer to this question, but over the last 40 years various criteria have been developed that can answer this…
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…
In stochastic models for queues and their networks, random events evolve in time. A process for their backward evolution is referred to as a time reversed process. It is often greatly helpful to view a stochastic model from two different…
A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole.…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
"Dynamic compensation" is a robustness property where a perturbed biological circuit maintains a suitable output [Karin O., Swisa A., Glaser B., Dor Y., Alon U. (2016). Mol. Syst. Biol., 12: 886]. In spite of several attempts, no fully…
The notion of homeostasis typically conceptualises biological and artificial systems as maintaining stability by resisting deviations caused by environmental and social perturbations. In contrast, (social) allostasis proposes that these…
New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying,…
We characterize completely the capacity for (nondegenerate) multistationarity of mass action reaction networks with one-dimensional stoichiometric subspace in terms of reaction structure. Specifically, we show that networks with two or more…
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…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect…
Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling…