相关论文: Flocking Regimes in a Simple Lattice Model

This survey focuses on the most important aspects of the mathematical theory of population genetic models of selection and migration between discrete niches. Such models are most appropriate if the dispersal distance is short compared to…

The modeling and investigation of the dynamics and configurations of animal groups is a subject of growing attention. In this paper, we present a continuum model of flocking and use it to investigate the reaction of a flock to an obstacle…

We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…

We present the first decentralized multi-copter flock that performs stable autonomous outdoor flight with up to 10 flying agents. By decentralized and autonomous we mean that all members navigate themselves based on the dynamic information…

We consider a size-structured aggregation and growth model of phytoplankton community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic biological phenomena in phytoplankton community such as growth, gravitational…

A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…

We study the collective dynamics of a lattice model of stochastically interacting agents with a weighted field of vision. We assume that agents preferentially interact with neighbours, depending on their relative location, through velocity…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…

I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all…

We propose a stochastic lattice gas model to describe the dynamics of two animal species population, one being a predator and the other a prey. This model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was performed by…

We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…

In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models…

When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…

We study properties of energy spreading in a lattice of elastically colliding harmonic oscillators (Ding-Dong model). We demonstrate that in the regular lattice the spreading from a localized initial state is mediated by compactons and…

We introduce a stochastic lattice gas model including two particle species and two parallel lanes. One lane with exclusion interaction and directed motion and the other lane without exclusion and unbiased diffusion, mimicking a micotubule…

The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We…

We study existence and stability of stationary solutions of a system of semilinear parabolic partial differential equations that occurs in population genetics. It describes the evolution of gamete frequencies in a geographically structured…

In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…

A toy model of particles packings is presented, which consists in arranging hexagons on a triangular lattice according to local stability rules. The number of stable packings is analytically computed and found to grow exponentially with the…