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) …

Every form of behaviour is shaped by trial and error. Such stepwise adaptation can occur
through individual learning or through natural selection, the basis of evolution. Since the …

[ ( hy)] Page 1 SIAM J. APPL. MATH. Vol. 55,No. pp. 763--783, June 1995 1995 Society for
Industrial and Applied Mathematics 011 GLOBAL STABILITY FOR A CLASS OF PREDATOR-PREY …

This paper considers a class of deterministic models of three interacting populations with a
view towards determining when all of the populations persist. In analytical terms persistence …

This paper deals with the question of uniqueness of limit cycles in predator-prey systems of
Gause type. By utilizing several transformations, these systems are reduced to a generalized …

In this work, we use an analytical approach to study the dynamic consequences of the
simplest forms of refuge use by the prey. Although this problem is not new, there are …

The main purpose of this paper is to develop criteria for which a simple food-chain model of
intermediate type and of arbitrary length has a globally stable positive equilibrium and to …

We investigate spreading properties of solutions of a large class of two-component reaction–
diffusion systems, including prey–predator systems as a special case. By spreading …

In this paper, a mathematical model for a predator–prey interaction with self and cross-
diffusion is proposed and analysed. Criteria for local stability, instability and global stability …

By considering the hunting cooperations, we propose a diffusive predator-prey model, in
which the function response is an increasing function in both predator and prey densities …