Dynamics of a predator-prey model

Sáez E.; Gonzalez-Olivares, E

Keywords: stability, models, bifurcation, ecosystems, predator-prey, asymptotic, mathematical, (mathematics)


We describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator-prey model proposed by R. M. May. In particular, we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear. Moreover, we show that locally symptotic stability of a positive equilibrium point does not imply global stability for this class of predator-prey models.

Más información

Título de la Revista: SIAM Journal on Applied Mathematics
Volumen: 59
Número: 5
Fecha de publicación: 1999
Página de inicio: 1867
Página final: 1878
URL: http://www.scopus.com/inward/record.url?eid=2-s2.0-0342298388&partnerID=q2rCbXpz