scholarly journals Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

2020 ◽  
pp. 1-31
Author(s):  
King-Yeung Lam ◽  
Shuang Liu ◽  
Yuan Lou
Keyword(s):  
Population Dynamics ◽  
Spatial Ecology ◽  
Recent Progress ◽  
Reaction Diffusion ◽  
Heterogeneous Environments ◽  
Epidemic Disease ◽  
Open Problems ◽  
Spatial Spread ◽  
Competition Models ◽  
River Models

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction–diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplanktongrowth, and spatial spread of epidemic disease. Open problems and conjectures are presented.P arts of this survey are adopted from the materials in [89,108,109], and some very recent progress are also included.

scholarly journals Modelling the spread of Wolbachia in spatially heterogeneous environments

2012 ◽  
Vol 9 (76) ◽  
pp. 3045-3054 ◽  
Author(s):  
Penelope A. Hancock ◽  
H. Charles J. Godfray
Keyword(s):  
Habitat Quality ◽  
Spatial Dynamics ◽  
Reaction Diffusion ◽  
Analytical Description ◽  
Host Population ◽  
Heterogeneous Environments ◽  
Spatial Spread ◽  
Density Dependent ◽  
Spatially Correlated ◽  
Reaction Diffusion Model

The endosymbiont Wolbachia infects a large number of insect species and is capable of rapid spread when introduced into a novel host population. The bacteria spread by manipulating their hosts' reproduction, and their dynamics are influenced by the demographic structure of the host population and patterns of contact between individuals. Reaction–diffusion models of the spatial spread of Wolbachia provide a simple analytical description of their spatial dynamics but do not account for significant details of host population dynamics. We develop a metapopulation model describing the spatial dynamics of Wolbachia in an age-structured host insect population regulated by juvenile density-dependent competition. The model produces similar dynamics to the reaction–diffusion model in the limiting case where the host's habitat quality is spatially homogeneous and Wolbachia has a small effect on host fitness. When habitat quality varies spatially, Wolbachia spread is usually much slower, and the conditions necessary for local invasion are strongly affected by immigration of insects from surrounding regions. Spread is most difficult when variation in habitat quality is spatially correlated. The results show that spatial variation in the density-dependent competition experienced by juvenile host insects can strongly affect the spread of Wolbachia infections, which is important to the use of Wolbachia to control insect vectors of human disease and other pests.

scholarly journals The influence of density in population dynamics with strong and weak Allee effect

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kamrun Nahar Keya ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Population Dynamics ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Logistic Growth ◽  
Allee Effects ◽  
Reaction Diffusion Model ◽  
Positive Steady States ◽  
The Stability ◽  
The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

scholarly journals Quantum chaos for point scatterers on flat tori

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120509 ◽  
Author(s):  
Henrik Ueberschär
Keyword(s):  
Wave Function ◽  
Strong Coupling ◽  
Quantum Chaos ◽  
Recent Progress ◽  
Three Dimensional ◽  
Point Scatterer ◽  
Open Problems ◽  
Survey Article ◽  
Delta Potential ◽  
Flat Tori

This survey article deals with a delta potential—also known as a point scatterer—on flat two- and three-dimensional tori. We introduce the main conjectures regarding the spectral and wave function statistics of this model in the so-called weak and strong coupling regimes. We report on recent progress as well as a number of open problems in this field.

scholarly journals An exact bifurcation diagram for a reaction–diffusion equation arising in population dynamics

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jerome Goddard II ◽  
Quinn A. Morris ◽  
Stephen B. Robinson ◽  
Ratnasingham Shivaji
Keyword(s):  
Population Dynamics ◽  
Diffusion Equation ◽  
Bifurcation Diagram ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation

scholarly journals Delta Scuti Stars: Selected Recent Highlights

2000 ◽  
Vol 176 ◽  
pp. 408-414
Author(s):  
G. Handler
Keyword(s):  
Recent Progress ◽  
Open Problems ◽  
Delta Scuti ◽  
Scuti Stars ◽  
Δ Scuti Stars

AbstractAn overview of recent progress in the research on δ Scuti stars is given. Some intriguing results and open problems are pointed out, and some ideas for future investigations are provided.

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