Nonuniqueness of limit cycles of gause-type predator-prey systems

Abstract

By comparison with the Lotka-Volterra system, we obtain a theorem concerning the nonuniqueness of limit cycles of a Gause-type predator-prey system The method we develope here can be generalized. Moreover, we disprove a conjecture posed by H.I. Freedman by constructing an example of a system with a strictly concave down prey isocline which has at least three limit cycles.

Keywords:

• Limit cycle
• Lotka-Vokerm syslem. Gause-type predator-prey system
• prey isocline

AMS(MOS)::

• 34C05
• 34C25
• 92A15