Some results on the dynamics generated by the Bazykin model

Abstract

A predator-prey model formerly proposed by A. Bazykin et al. [Bifurcation diagrams of planar dynamical systems (1985)] is analyzed in the case when two of the four parameters are kept fixed. Dynamics and bifurcation results are deduced by using the methods developed by D. K. Arrowsmith and C. M. Place [Ordinary differential equations (1982)], S.-N. Chow et al. [Normal forms and bifurcation of planar fields (1994)], Y. A. Kuznetsov [Elements of applied bifurcation theory (1998)], and A. Georgescu [Dynamic bifurcation diagrams for some models in economics and biology (2004)]. The global dynamic bifurcation diagram is constructed and graphically represented. The biological interpretation is presented, too.