Convergent activation dynamics in continuous time networks

MW Hirsch - Neural networks, 1989 - Elsevier
The activation dynamics of nets are considered from a rigorous mathematical point of view.
A net is identified with the dynamical system defined by a continuously differentiable vector …

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] Evolutionary games and population dynamics

J Hofbauer, K Sigmund - 1998 - books.google.com
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 …

[图书][B] Nonlinear dynamics of interacting populations

AD Bazykin - 1998 - World Scientific
In this chapter we study models for the growth of a single population. Some of these models
will be used in the sequel as constituents for models of interacting popula tions …

Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system

F Yi, J Wei, J Shi - Journal of Differential Equations, 2009 - Elsevier
A diffusive predator–prey system with Holling type-II predator functional response subject to
Neumann boundary conditions is considered. Hopf and steady state bifurcation analysis are …

Global stability for a class of predator-prey systems

SB Hsu, TW Huang - SIAM Journal on Applied Mathematics, 1995 - SIAM
[ ( 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 …

Persistence in models of three interacting predator-prey populations

HI Freedman, P Waltman - Mathematical biosciences, 1984 - Elsevier
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 …

Uniformly persistent systems

G Butler, HI Freedman, P Waltman - Proceedings of the American …, 1986 - JSTOR
Uniformly Persistent Systems Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL
SOCIETY Volume 96, Number 3, March 1986 UNIFORMLY PERSISTENT SYSTEMS …

Predator–prey system with strong Allee effect in prey

J Wang, J Shi, J Wei - Journal of Mathematical Biology, 2011 - Springer
Global bifurcation analysis of a class of general predator–prey models with a strong Allee
effect in prey population is given in details. We show the existence of a point-to-point …

The dynamical systems approach to differential equations

MW Hirsch - Bulletin of the American mathematical society, 1984 - ams.org
Every mathematician has a particular way of thinking about mathematics, but rarely makes it
explicit. Yet such perspectives, in any particular field, can be of great value to nonexperts …