41 citations · 195 across the 19 of their papers we have counts for
19 papers
A flux-based approach for analyzing the disguised toric locus of reaction networks
Balázs Boros, Gheorghe Craciun, Oskar Henriksson +2
Dynamical systems with polynomial right-hand sides are very important in various applications, e.g., in biochemistry and population dynamics. The mathematical study of these dynami…
Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity
Murad Banaji, Balázs Boros, Josef Hofbauer
In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadrati…
The inheritance of local bifurcations in mass action networks
Murad Banaji, Balázs Boros, Josef Hofbauer
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 ad…
Oscillations in three-reaction quadratic mass-action systems
Murad Banaji, Balázs Boros, Josef Hofbauer
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 w…
The smallest bimolecular mass-action system with a vertical Andronov-Hopf bifurcation
Murad Banaji, Balázs Boros, Josef Hofbauer
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 invarian…
The smallest bimolecular mass action reaction networks admitting Andronov-Hopf bifurcation
Murad Banaji, Balázs Boros
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 bifur…
Limit cycles in mass-conserving deficiency-one mass-action systems
Balázs Boros, Josef Hofbauer
We present some simple mass-action systems with limit cycles that fall under the scope of the Deficiency-One Theorem. All the constructed examples are mass-conserving and their sto…
Some minimal bimolecular mass-action systems with limit cycles
Balázs Boros, Josef Hofbauer
We discuss three examples of bimolecular mass-action systems with three species, due to Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium which…
Adding species to chemical reaction networks: preserving rank preserves nondegenerate behaviours
Murad Banaji, Balázs Boros, Josef Hofbauer
We show that adding new chemical species into the reactions of a chemical reaction network (CRN) in such a way that the rank of the network remains unchanged preserves its capacity…
Oscillations in planar deficiency-one mass-action systems
Balázs Boros, Josef Hofbauer
Whereas the positive equilibrium of a mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly invo…
Weakly reversible mass-action systems with infinitely many positive steady states
Balázs Boros, Gheorghe Craciun, Polly Y. Yu
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 o…
Complex-balanced equilibria of generalized mass-action systems: Necessary conditions for linear stability
Balazs Boros, Stefan Müller, Georg Regensburger
It is well known that, for mass-action systems, complex-balanced equilibria are asymptotically stable. For generalized mass-action systems, even if there exists a unique complex-ba…
Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage Class
Balázs Boros, Josef Hofbauer
We give a new proof of the fact that each weakly reversible mass-action system with a single linkage class is permanent.
Planar S-systems: Permanence
Balázs Boros, Josef Hofbauer
We characterize permanence of planar S-systems. Further, we construct a planar S-system with three limit cycles.
Existence of Positive Steady States for Weakly Reversible Mass-Action Systems
Balázs Boros
We prove the following. For each weakly reversible mass-action system, there exists a positive steady state in each positive stoichiometric class.
Planar S-systems: Global stability and the center problem
Balázs Boros, Josef Hofbauer, Stefan Müller +1
S-systems are simple examples of power-law dynamical systems (polynomial systems with real exponents). For planar S-systems, we study global stability of the unique positive equili…
The center problem for the Lotka reactions with generalized mass-action kinetics
Balázs Boros, Josef Hofbauer, Georg Regensburger +1
Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions and the resulting planar…
On global stability of the Lotka reactions with generalized mass-action kinetics
Balázs Boros, Josef Hofbauer, Stefan Müller
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…
On the dependence of the existence of the positive steady states on the rate coefficients for deficiency-one mass action systems: single linkage class
Balázs Boros
The Deficiency-One Theorem states that there exists a unique positive steady state in each positive stoichiometric class for weakly reversible deficiency-one mass action systems wi…