Exclusion type spatially heterogeneous processes in continuum

Global behavior of N competing species with strong diffusion: diffusion leads to exclusion

It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an heterogeneous environment. We propose a spatially heterogeneous system modeling the competition of several species for a single resource. If spatial movements are fast enough, we show that our system can be well approximated by a spatially homogeneous system, called aggregated model, which can be explicitly computed. Moreover, we show that if the competitive ex…

On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populations

The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The differences between the two populations are the diffusion strategy and the harvesting intensity. In the absence of harvesting, competing populations may either coexist, or one of them may bring the other to extinction. If the latter is the case, introduction of any level of harvesting to the successful species guarantees survival to its non-harv…

The stability and Hopf bifurcation of the diffusive Nicholson's blowflies model in spatially heterogeneous environment

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 death rate affects the dynamics of the model. The unique positive steady state is locally asymptotically stable if the ratio is less than a critical value. However, when the ratio is greater than the critical value, large time delay can make the unique positive steady state unstable through Hopf bifurcation. Especially, the first Hopf bifurcation value tend…

空间异质世界中的临界转变路径优化

Optimisation of tipping pathways in a spatially heterogeneous world

针对空间扩展系统中的临界转变问题，提出一个约束优化框架，通过局部干预（如修改临界阈值和控制前沿动力学）来最大化系统恢复力或促进理想状态恢复，并在Allen-Cahn方程中验证了其有效性。

一类具有非线性空间异质交叉扩散的通用Lotka-Volterra系统的存在性与渐近稳定性

Existence and asymptotic stability of a generic Lotka-Volterra system with nonlinear spatially heterogeneous cross-diffusion

本文针对具有空间异质捕食函数和趋化系数的Lotka-Volterra系统，引入加权范数并推广不等式，结合能量估计和bootstrap方法证明了解的存在性，并利用推广的LaSalle原理分析了常数平衡点的渐近稳定性。

The role of harvesting and growth rate for spatially heterogeneous populations

This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are developed based on this clause instead of random choice. We prove the existence and uniqueness of the solution to the model we consider. Theoretically, we state that when species coexist, one may drive the other to die out, and both species extinct, considering all possible rational values of parameters. These results highlight a comparative study between two ha…