The theory of limiting similarity

P Abrams - Annual review of ecology and systematics, 1983 - JSTOR
The theory of limiting similarity is an outgrowth of the competitive exclusion principle. Until
recently [ie before the work of Armstrong & McGehee (13, 14)], the competitive exclusion …

A survey of constructing Lyapunov functions for mathematical models in population biology

SB Hsu - Taiwanese Journal of Mathematics, 2005 - JSTOR
In this paper we survey the construction of Lyapunov functions (or functional) for various
ecological models which take the form of ODE systems (or Reaction-Diffusion PDE systems) …

[图书][B] The theory of the chemostat: dynamics of microbial competition

HL Smith, P Waltman - 1995 - books.google.com
The chemostat is a basic piece of laboratory apparatus, yet it has begun to occupy an
increasingly central role in ecological studies. The ecological environment created by a …

[图书][B] Elements of mathematical ecology

M Kot - 2001 - books.google.com
Elements of Mathematical Ecology provides an introduction to classical and modern
mathematical models, methods, and issues in population ecology. The first part of the book …

Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics

X Bai, M Winkler - Indiana University Mathematics Journal, 2016 - JSTOR
The fully parabolic two-species chemotaxis system (∗) u_t=d_1Δu-χ_1\triangledown⋅(u\
triangledownw)+μ_1u(1-u-a_1v)\quadx∈Ω,t\textgreater0,\v_t=d_2Δv-χ_2\triangledown⋅(v …

Competitive exclusion

RA Armstrong, R McGehee - The American Naturalist, 1980 - journals.uchicago.edu
Recent developments in the mathematical theory of competitive exclusion are discussed
and placed in historical perspective. The models which have been used in theoretical …

[图书][B] Diffusion, self-diffusion and cross-diffusion

Y Lou - 1995 - search.proquest.com
In 1979, Shigesada et al. proposed a mathematical model in which the movements of two
competing species are also affected by, besides diffusion, the population pressures, which …

Global dynamics of the Lotka‐Volterra competition‐diffusion system: diffusion and spatial heterogeneity I

X He, WM Ni - Communications on Pure and Applied …, 2016 - Wiley Online Library
In the first part of this series of three papers, we investigate the combined effects of diffusion,
spatial variation, and competition ability on the global dynamics of a classical Lotka‐Volterra …

[图书][B] Constructions of strict Lyapunov functions

M Malisoff, F Mazenc - 2009 - books.google.com
The construction of strict Lyapunov functions is a challenging problem that is of significant
ongoing research interest. Although converse Lyapunov function theory guarantees the …

[图书][B] Management and analysis of biological populations

BS Goh - 2012 - books.google.com
Management and Analysis of Biological Populations demonstrates the usefulness of optimal
control theory in the management of biological populations and the Liapunov function in …