Global stability of Gause-type predator-prey systems (Q1174281)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Global stability of Gause-type predator-prey systems |
scientific article; zbMATH DE number 8481
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global stability of Gause-type predator-prey systems |
scientific article; zbMATH DE number 8481 |
Statements
Global stability of Gause-type predator-prey systems (English)
0 references
25 June 1992
0 references
The following class of Gauss-type predator-prey models is considered \[ x'=xg(x)-\xi(y)p(x),\qquad y'=\eta(y)(-\gamma + q(x)),\leqno(1) \] where \(x(t)\) amd \(y(t)\) represent the prey and predator populations, respectively. The main aim of this paper is addressed to obtaining sufficient conditions under which the system (1) has a global asymptotically stable nontrivial equilibrium solution. Results are obtained via comparison techniques and Bendixson-Dulac's criterion.
0 references
global stability
0 references
limit cycles
0 references
Gauss-type predator-prey models
0 references
global asymptotically stable nontrivial equilibrium solution
0 references
comparison techniques
0 references
Bendixson-Dulac's criterion
0 references
