相关论文: Some minimal bimolecular mass-action systems with …

This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of at least continuous state feedback laws. This is the case of nonholonomic mechanical systems, an example being the…

This paper is concerned with the existence and mass concentration behavior of minimizers for rotating Bose-Einstein condensations (BECs) with attractive interactions in a bounded domain $\mathcal{D}\subset \mathbb{R}^2$. It is shown that,…

The simplest ring oscillator is made from three strongly nonlinear elements repressing each other unidirectionally resulting in the emergence of a limit cycle. A popular implementation of this scheme uses repressive genes in bacteria…

Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model…

We consider large spin systems with short-range ferromagnetic interactions and long-range antiferromagnetic interactions subjected to periodic boundary conditions which have been proved by Giuliani, Lebowitz and Lieb to have minimizers that…

Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…

We analyze the driven-dissipative dynamics of subwavelength periodic atomic arrays in free space, where atoms interact via light-induced dipole-dipole interactions. We find that depending on the system parameters, the underlying mean-field…

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 invariant two-dimensional surface that is filled with periodic…

We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a…

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…

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…

The Brusselator is a generic reaction-diffusion model for a tri-molecular chemical reaction. We consider the case when the input and output reactions are slow. In this limit, we show the existence of $K$-periodic, spatially bi-stable…

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to…

In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…

Two-dimensional (2D) systems have attracted renewed interest within the scientific community due to their anomalous dynamical behaviors, which arise from long-wavelength density fluctuations as predicted by the Mermin-Wagner-Hohenberg (MWH)…

Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion [1,2,3].…

This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…

We investigate a kinetic model for interacting particles whose masses are integer multiples of an elementary mass. These particles undergo binary collisions which preserve momentum and energy but during which some number of elementary…

Self-sustained dynamical phases of living matter can exhibit remarkable similarities over a wide range of scales, from mesoscopic vortex structures in microbial suspensions and motility assays of biopolymers to turbulent large-scale…

The paper is concerned with the study of a control system consisting of one major agent and many identical minor agents in the limit case when the number of agents tends to infinity. To study the limiting system we use the mean field…