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 …

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) …

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 …

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 …

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 …

Recent developments in the mathematical theory of competitive exclusion are discussed
and placed in historical perspective. The models which have been used in theoretical …

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 …

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 …

The construction of strict Lyapunov functions is a challenging problem that is of significant
ongoing research interest. Although converse Lyapunov function theory guarantees the …

Management and Analysis of Biological Populations demonstrates the usefulness of optimal
control theory in the management of biological populations and the Liapunov function in …