相关论文: On global stability of the Lotka reactions with ge…

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 ODE. We characterize the parameters (positive coefficients…

A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…

Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems…

Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…

We consider delayed chemical reaction networks with generalized kinetics of product form and show that complex balancing implies that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is…

Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics…

Dynamical systems arising from chemical reaction networks with mass action kinetics are the subject of chemical reaction network theory (CRNT). In particular, this theory provides statements about uniqueness, existence, and stability of…

Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative power-law rate functions and serves as a more realistic…

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 degree, including negative and non-integer degree. We…

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 dynamical systems can be generated by many different reaction…

Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the…

We establish that mass conserving single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This result holds for closed systems without…

Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…

A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…

This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of Chemical Reaction…

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 with mass action kinetics. We obtain a sufficient condition…

We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems that are known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More…

Robustness against the presence of environmental disruptions can be observed in many systems of chemical reaction network. However, identifying the underlying components of a system that give rise to robustness is often elusive. The…

This paper studies the solutions of a reaction--diffusion system with nonlinearities that generalise the Lengyel--Epstein and FitzHugh--Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the…

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give…