相关论文: Global dynamics of a two-stage structured diffusiv…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
We revisit a model proposed by Freedman etal in \cite{freedman} which describes the dynamics of a population diffusing in a patchy environment. From their work it is known that positive steady states exist for this model, but not whether…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…
In this paper, a single population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
This paper is concerned with the two-dimensional chemotaxis-fluid model \begin{equation*} \begin{cases} n_t+u\cdot\nabla n=\Delta (n\phi(v))+\mu n(1-n),\\ v_t+u\cdot\nabla v=\Delta v-nv,\\ u_t+ \kappa (u\cdot\nabla) u=\Delta…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
We investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linear equations for a set of auxiliary linear…
We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models arise in a variety of contexts from climate change to…
This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under…
We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…
The current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains. We first prove the global existence and boundedness of…
In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the…