Multiplicity and stability of a predator–prey model with non-monotonic conversion rate

✍ Scribed by Hua Nie; Jianhua Wu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 457 KB
• Volume: 10
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2007.08.020

✦ Synopsis

This paper is concerned with a predator-prey model possessing a non-monotonic conversion rate. The main purpose is to determine the multiple existence and stability of positive steady-state solutions to this system. The results show that if the parameter d is suitably large, then the system contains an S-shaped global bifurcation curve with respect to a bifurcation parameter. That is, the system has two or three positive solutions for a suitable range of parameters. Moreover, the stability of positive solutions on this curve is also given. If d is properly small, both uniqueness and non-uniqueness results can occur. The main tools used here include the bifurcation theory, the Lyapunov-Schmidt procedure, and the perturbation technique.