Related papers: Bifurcations in planar, quadratic mass-action netw…
We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable of Andronov-Hopf bifurcation (from here on abbreviated to "Hopf bifurcation"). It is easily shown that any such network must have…
It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes…
We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a…
We present a three-dimensional differential equation, which robustly displays a degenerate Andronov-Hopf bifurcation of infinite codimension, leading to a center, i.e., an invariant two-dimensional surface that is filled with periodic…
For the reaction networks with zero-one stoichiometric coefficients (or simply zero-one networks), we prove that if a network admits a Hopf bifurcation, then the rank of the stoichiometric matrix is at least four. As a corollary, we show…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the…
We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total…
A multistationarity region is the part of a reaction network's parameter space that gives rise to multiple steady states. Mathematically, this region consists of the positive parameters for which a parametrized family of polynomial…
Steady states are frequently used to investigate the long-term behaviors of (bio)-chemical systems. Recently, there has been a growing interest in network-based approaches due to their efficiency in deriving parametrizations of positive…
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…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we…
Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state; while some networks exhibit absolute concentration robustness (ACR), which means that some species…
Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult,…
The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo qualitative changes, known as Morse bifurcations, and to exist for a large range of energies, not just immediately above…
Mutation is introduced into autocatalytic reaction networks. Examples of low dimensional dynamical systems --- n = 2, 3 and 4 --- are discussed and complete qualitative analysis is presented. Error thresholds known from simple…
For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breaking bifurcations that can emerge when two bulk diffusing species are coupled to two-component nonlinear intracellular reactions that are restricted to occur only within…
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…
Phosphorylation networks, representing the mechanisms by which proteins are phosphorylated at one or multiple sites, are ubiquitous in cell signalling and display rich dynamics such as unlimited multistability. Dual-site phosphorylation…