27 citations · 144 across the 15 of their papers we have counts for
17 papers
Stability and Fluctuations in Complex Ecological Systems
Eric Forgoston, Sarah Day, Peter C. de Ruiter +24
From 08-12 August, 2022, 32 individuals participated in a workshop, Stability and Fluctuations in Complex Ecological Systems, at the Lorentz Center, located in Leiden, The Netherla…
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…
Permanence via invasion graphs: Incorporating community assembly into Modern Coexistence Theory
Josef Hofbauer, Sebastian J. Schreiber
To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to av…
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…
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.
On the bijectivity of families of exponential/generalized polynomial maps
Stefan Müller, Josef Hofbauer, Georg Regensburger
We start from a parametrized system of generalized polynomial equations (with real exponents) for positive variables, involving generalized monomials with positive…
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…
Genetic Recombination as a Chemical Reaction Network
Stefan Müller, Josef Hofbauer
The process of genetic recombination can be seen as a chemical reaction network with mass-action kinetics. We review the known results on existence, uniqueness, and global stabilit…
Robust permanence for interacting structured populations
Josef Hofbauer, Sebastian J. Schreiber
The dynamics of interacting structured populations can be modeled by where , , and are matrices with non-…
Time averages, recurrence and transience in the stochastic replicator dynamics
Josef Hofbauer, Lorens A. Imhof
We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an avera…