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Global Qualitative Analysis for a Ratio-Dependent Predator–Prey Model with Delay
- Source :
-
Journal of Mathematical Analysis & Applications . Feb2002, Vol. 266 Issue 2, p401. 19p. - Publication Year :
- 2002
-
Abstract
- A ratio-dependent predator–prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system and, therefore, does not imply global asymptotic stability. It is found that an orbitally asymptotically stable periodic orbit exists in that model. Some sufficient conditions which guarantee the global stability of positive equilibrium are given. [Copyright &y& Elsevier]
- Subjects :
- *DELAY differential equations
*ASYMPTOTIC expansions
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 266
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 8496584
- Full Text :
- https://doi.org/10.1006/jmaa.2001.7751