(Predator-prey model) Odell (1980) considered the system ẋ=x[x(1-x)-y], ŷ=y(x-a) where x ≥0 is the dimensionless population of the prey, y ≥0 is the dimension- less population of the predator, and a ≥0 is a control parameter. a) Sketch the nullelines in the first quadrant x, y ≥0. b) Show that the fixed points are (0,0),(1,0), and (a, a-a^2), and classify them. c) Sketch the phase portrait for a>1, and show that the predators go extinct. d) Show that a Hopf bifurcation occurs at ae=±. Is it su

Lotka-Volterra, Predator-Prey Model - SlideServe

Lotka Volterra Regeln • Populationsdynamik