Related papers: The continuous-time frog model can spread arbitrar…
To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…
This paper deals with a free boundary problem of the Lotka-Volterra type prey-predator model with variable intrinsic growth rate for predator over a one dimensional habitat, in which the free boundary represents the spreading front and is…
We consider a slight modification of the frog model. For a given graph, each vertex has $\mathrm{Poisson}(\lambda)$ particles (or frogs). At time zero, only the particles at the origin are active, and all the other particles are sleeping.…
We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which…
In this paper we study a ratio-dependent predator-prey model with a free boundary causing by both prey and predator over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing…
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous time simple random walk on the d-dimensional lattice. These particles are called A-particles and move independently…
We consider open multi-agent systems, which are systems subject to frequent arrivals and departures of agents while the studied process takes place. We study the behavior of all-to-all pairwise gossip interactions in such open systems.…
In this paper we consider a free boundary problem which models the spreading of an invasive species whose spreading is enhanced by the changing climate. We assume that the climate is shifting with speed c and obtain a complete…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
We present the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface, and many of its predictions for experiment. We find that such systems are stable, and have long-range orientational order, over a…
The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
We consider a random interacting particle system, known as the frog model, on infinite Galton-Watson trees allowing offspring zero and one. The system starts with one awake particle (frog) at the root of the tree and a random number of…
In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…
Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…
We introduce a model of simple type theory with potential infinite carrier sets. The functions in this model are automatically continuous, as defined in this paper. This notion of continuity does not rely on topological concepts, including…