9 citations · 16 across the 14 of their papers we have counts for
12 papers · 1 filter
Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems
Diego Rojas La Luz, Gheorghe Craciun, Polly Y. Yu
We study the global stability of generalized Lotka-Volterra systems with generalized polynomial right-hand side, without restrictions on the number of variables or the polynomial d…
Global stability of perturbed complex-balanced systems
Polly Y. Yu
A class of polynomial dynamical systems called complex-balanced are locally stable and conjectured to be globally stable. In general, complex-balancing is not a robust property, i.…
An algorithm for finding weakly reversible deficiency zero realizations of polynomial dynamical systems
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
Systems of differential equations with polynomial right-hand sides are very common in applications. On the other hand, their mathematical analysis is very challenging in general, d…
The disguised toric locus and affine equivalence of reaction networks
Sabina J. Haque, Matthew Satriano, Miruna-Stefana Sorea +1
Under the assumption of mass-action kinetics, a dynamical system may be induced by several different reaction networks and/or parameters. It is therefore possible for a mass-action…
A graph-theoretic condition for delay stability of reaction systems
Gheorghe Craciun, Maya Mincheva, Casian Pantea +1
Delay mass-action systems provide a model of chemical kinetics when past states influence the current dynamics. In this work, we provide a graph-theoretic condition for delay stabi…
Autocatalytic systems and recombination: a reaction network perspective
Gheorghe Craciun, Abhishek Deshpande, Badal Joshi +1
Autocatalytic systems are very often incorporated in the "origin of life" models, a connection that has been analyzed in the context of the classical hypercycles introduced by Manf…
Uniqueness of weakly reversible and deficiency zero realizations of dynamical systems
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
A reaction network together with a choice of rate constants uniquely gives rise to a system of differential equations, according to the law of mass-action kinetics. On the other ha…
Single-Target Networks
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
We characterize the dynamics of all single-target networks under mass-action kinetics: either the system is (i) globally stable for all choice of rate constants (in fact, dynamical…
Delay stability of reaction systems
Gheorghe Craciun, Maya Mincheva, Casian Pantea +1
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks wi…
Realizations of kinetic differential equations
G. Craciun, M. D. Johnston, G. Szederkényi +3
The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is…
An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dyn…
A generalization of Birch's theorem and vertex-balanced steady states for generalized mass-action systems
Gheorghe Craciun, Stefan Muller, Casian Pantea +1
Mass-action kinetics and its generalizations appear in mathematical models of (bio-)chemical reaction networks, population dynamics, and epidemiology. The dynamical systems arising…