Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0872.34047
Zhao, Tao; Kuang, Yang; Smith, H.L.
Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 28, No.8, 1373-1394 (1997). ISSN 0362-546X

The authors consider the following delayed Gause-type predator-prey system \align \dot x(t)&= x(t)[g(x(t))- p(x(t))y(t)],\\ \dot y(t)&= y(t)[-\nu+ h(x(t-\tau))], \endalign where $x(t),y(t)$ denote the population density of prey and predator at time $t$, respectively, the positive constant $\nu$ stands for the death rate of predator $y$ in the absence of prey $x$, and $\tau$ is the recover-time. The main goal of the paper is to establish global existence of nonconstant periodic solutions. This is done by proving the existence of nontrivial fixed points of an appropriate map. In the last section of the paper the authors apply their results to the following delayed Lotka-Volterra predator-prey system \align \dot x(t)&= x(t)\Biggl[ \gamma-ax(t)- \frac{by(t)} {1+cx(t)}\Biggr],\\ \dot y(t)&= y(t)\Biggl[ -\nu+ \frac{dx(t-\tau)} {1+cx(t-\tau)}\Biggr]. \endalign{}.
[V.Petrov (Plovdiv)]
MSC 2000:
*34K13 Periodic solutions of functional differential equations
34C25 Periodic solutions of ODE
92D25 Population dynamics

Keywords: delayed Gause-type predator-prey system; nonconstant periodic solutions; delayed Lotka-Volterra predator-prey system

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster