Related papers: Influence of density-dependent diffusion on patter…
Incorporating free boundary into time-delayed reaction-diffusion equations yields a compatible condition that guarantees the well-posedness of the initial value problem. With the KPP type nonlinearity we then establish a vanishing-spreading…
This chapter focuses on the derivation of a doubly nonlocal Fisher-KPP model, which is a macroscopic nonlocal evolution equation describing population dynamics in the large population limit. The derivation starts from a microscopic…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…
In this paper we consider a reaction-diffusion equation of Fisher-KPP type inside an infinite cylindrical domain in $\mathbb{R}^{N+1}$, coupled with a reaction-diffusion equation on the boundary of the domain, where potentially fast…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a…
Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatio-temporal spreading into areas occupied by…
The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource…
The role of dispersal on the stability and synchrony of a metacommunity is a topic of considerable interest in theoretical ecology. Dispersal is known to promote both synchrony, which enhances the likelihood of extinction, and spatial…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is non-local, and show that spatial structures with interesting…
We investigate the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals, and the saturation factor is…
Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and…
Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in…
We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines state-structured local demography (specified by an integral or matrix projection model)…
Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…