Bifurcation analysis of a predator-prey system involving group defence. (English) Zbl 0657.92015

Wolkowicz, G. S. K.

SIAM J. Appl. Math. 48, No. 3, 592-606 (1988).

The carrying capacity k of the environment for the prey-predator interaction model with group defence of the form \[ \dot x=x g(x,k)-y p(x),\quad \dot y=y(-s+q(x)) \] is considered as a parameter to discuss the structure of the solutions. A good analysis of the model is exhibited and among others Hopf bifurcation, convergence and extinction of the predator coming from too much enrichment of the environment are investigated.

Reviewer: G.Karakostas

MSC:

92D25	Population dynamics (general)
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
92D40	Ecology
37-XX	Dynamical systems and ergodic theory
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

carrying capacity; prey-predator interaction model; group defence; Hopf bifurcation; convergence; extinction