Related papers: Survival and complete convergence for a spatial br…
We consider the problem of completely covering an unknown discrete environment with a swarm of asynchronous, frequently-crashing autonomous mobile robots. We represent the environment by a discrete graph, and task the robots with occupying…
The symbiotic branching model describes a spatial population consisting of two types that are allowed to migrate in space and branch locally only if both types are present. We continue our investigation of the large scale behaviour of the…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows…
We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…
Let $(Z_n)$ be a supercritical branching process in a random environment $\xi$. We study the convergence rates of the martingale $W_n = Z_n/ E[Z_n| \xi]$ to its limit $W$. The following results about the convergence almost sur (a.s.), in…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\kappa}_v$ which takes the value $j\in \{0,1,2,3\}$ with probability…
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…
We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…
The (strong and weak) well-posedness is proved for singular SDEs depending on the distribution density point-wisely and globally, where the drift satisfies a local integrability condition in time-spatial variables, and is Lipschitz…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed by balls connected with thin corridors, we show the occurrence of pattern…
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…
The spatial logistic branching process is a population dynamics model in which particles move on a lattice according to independent simple symmetric random walks, each particle splits into a random number of individuals at rate one, and…
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…
A microscopic model is developed, within the frame of the theory of quantitative traits, to study both numerically and analytically the combined effect of competition and assortativity on the sympatric speciation process, i.e. speciation in…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…