相关论文: Global dynamics of a two-stage structured diffusiv…

This paper explores a non-linear, non-local model describing the evolution of a single species. We investigate scenarios where the spatial domain is either an arbitrary bounded and open subset of the $n$-dimensional Euclidean space or a…

We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial…

The paper is concerned with the effect of the spatio-temporal heterogeneity on the principal eigenvalue of some linear time-periodic parabolic system. Various asymptotic behaviors of the principal eigenvalue and its monotonicity, as a…

I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…

This paper is devoted to a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat, where the seasonal succession accounts for the effect of two different seasons. Firstly, we provide the…

The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…

The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…

We present a first-principles formalism for studying dynamical heterogeneities in glass forming liquids. Based on the Non-Equilibrium Self-Consistent Generalized Langevin Equation theory, we were able to describe the time-dependent local…

We study the diffusive logistic equation with a free boundary in timeperiodic environment. To understand the effect of the dispersal rate $d$, the original habitat radius $h_0$, the spreading capability $\mu$, and the initial density $u_0$…

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to…

We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…

We consider a parameter dependent periodic-logistic problem with a logistic term involving a degeneracy that replicates time dependent refuges in the habitat of a population. Working under no or very minimal assumptions on the boundary…

Microbiomes are complex systems comprised of many interacting species. Species can survive harsh or changing conditions by rapid adaptation, a process accelerated by the exchange of genetic material between different species through…

Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their…

In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…

This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…

Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law…

In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the…

A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…

We study the long time behavior of a parabolic Lotka-Volterra type equation considering a time-periodic growth rate with non-local competition. Such equation describes the dynamics of a phenotypically struc-tured population under the effect…