Related papers: Localization for a Class of Linear Systems
We consider a discrete-time stochastic growth model on the $d$-dimensional lattice with non-negative real numbers as possible values per site. The growth model describes various interesting examples such as oriented site/bond percolation,…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. We remark that the diffusive scaling limit proven in our previous work [Nagahata, Y.,…
We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…
We study branching random walks in random environment on the $d$-dimensional square lattice, $d \geq 1$. In this model, the environment has finite range dependence, and the population size cannot decrease. We prove limit theorems (laws of…
In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we…
We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the…
We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider in particular a…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their boundaries. Each site of the space may contain only one…
We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
A two-species spatially extended system of hosts and parasitoids is studied. There are two distinct kinds of coexistence; one with populations distributed homogeneously in space and another one with spatiotemporal patterns. In the latter…
We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…