相关论文: Limit cycles in mass-conserving deficiency-one mas…

Unlike typical condensed-matter systems, ultra-cold atoms loaded into optical lattices allow separate control of both the particle number and system size. As a consequence, there are two distinct "thermodynamic" limits that can be defined…

Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…

In recent decades, several mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed. We demonstrate that it is not possible to establish the existence, uniqueness, and stability of a limit…

We study nonequilibrium phase transitions in a mass-aggregation model which allows for diffusion, aggregation on contact, dissociation, adsorption and desorption of unit masses. We analyse two limits explicitly. In the first case mass is…

This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…

Understanding when linear immersions of nonlinear dynamical systems exist is important since such immersions allow us to leverage the rich tools of linear system theory to analyze nonlinear dynamics. Recently, Liu et al. (2023) showed that…

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 admitting a local bifurcation of equilibria, assuming only a…

We study a stochastic two-species chemical reaction system with two mechanisms. One mechanism consists of chemical interactions which govern the overall drift of species amounts in the system; the other mechanism consists of resampling,…

Biochemical oscillations are prevalent in living organisms. Systems with a small number of constituents cannot sustain coherent oscillations for an indefinite time because of fluctuations in the period of oscillation. We show that the…

Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state; while some networks exhibit absolute concentration robustness (ACR), which means that some species…

The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under…

We analyze the mathematical properties of a multi-species biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet-Neumann boundary conditions on a bounded domain. This model belongs to the class of…

We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…

We develop a model-independent reduction method of chemical reaction systems based on the stoichiometry, which determines their network topology. A subnetwork can be eliminated systematically to give a reduced system with fewer degrees of…

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds.…

We introduce a model of three-species two-particle diffusion-limited reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three persistence parameters (survival probabilities in reaction) of the hopping particle. We consider…

We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or…

The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a…

We consider a class of multi-agent distributed synchronization systems, which are modeled as $n$ particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in [15], employing so-called…

We establish an existence result for weak solutions to an aggregation-diffusion-reaction equation with a constraint, arising in the modelling of multiple sclerosis. The model is derived from a general chemotaxis-type framework and describes…