相关论文: Existence of Positive Steady States for Weakly Rev…

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 of systems whose underlying reaction network is reversible…

We give a new proof of the fact that each weakly reversible mass-action system with a single linkage class is permanent.

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 with one linkage class (regardless of the values of the rate…

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…

We show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess infinitely many steady states. We provide a few examples in two dimensions and an example in three dimensions that…

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…

Power law systems have been studied extensively due to their wide-ranging applications, particularly in chemistry. In this work, we focus on power law systems that can be decomposed into stoichiometrically independent subsystems. We show…

The Cauchy problem for the attraction-repulsion chemotaxis system in the whole $n$-dimensional space has uncountable constant steady states. In the attraction chemotaxis system, each positive constant steady state is stable if it is in a…

It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so…

We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states…

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…

A frequently desirable characteristic of chemical kinetics systems is that of persistence, the property that if all the species are initially present then none of them may tend toward extinction. It is known that solutions of…

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 hand, different networks can generate the same dynamical…

For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to…

Using a structure theorem from [FG2010] we prove a version of multiple recurrence for sets of positive measure in a general stationary dynamical system.

We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we…

We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.

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-balanced equilibrium (in every stoichiometric class and for…

Given a dynamical system with polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some network properties may guarantee specific dynamical properties,…

We prove the existence and nonlinear stability of steady states of the Vlasov-Poisson system in the stellar dynamics case. The steady states are obtained as minimizers of an energy-Casimir functional from which fact their dynamical…