Exercise 4. (Rabbits vs. Foxes) The Lotka-Volterra predator prey model is given by the system R = aR – bRF, F = -cF + dRF, with parameters a, b, c, d > 0 and R(t) population of rabbits in time, and F(t) population of foxes in time. a) Discuss the biological meaning of each term in the equations and comment on any unrealistic assumptions. b) show that the model can be rewritten (adimensionalization) as i = ¤(1 – y), ÿ = py(I - 1). c) Find a conserved quantity in terms of the dimansionless variables in (b). |3D

Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
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Exercise 4.
(Rabbits vs. Foxes) The Lotka-Volterra predator
prey model is given by the system R = aR – bRF, F = -cF + dRF, with parameters
a, b, c, d > 0 and R(t) population of rabbits in time, and F(t) population of foxes in time.
a) Discuss the biological meaning of each term in the equations and comment on any
unrealistic assumptions.
b) show that the model can be rewritten (adimensionalization) as i= ¤(1 – y), ý =
py(I – 1).
c) Find a conserved quantity in terms of the dimansionless variables in (b).
d) Show that the model predicts cycles in the population of both species for almost all
initial conditions.
Transcribed Image Text:Exercise 4. (Rabbits vs. Foxes) The Lotka-Volterra predator prey model is given by the system R = aR – bRF, F = -cF + dRF, with parameters a, b, c, d > 0 and R(t) population of rabbits in time, and F(t) population of foxes in time. a) Discuss the biological meaning of each term in the equations and comment on any unrealistic assumptions. b) show that the model can be rewritten (adimensionalization) as i= ¤(1 – y), ý = py(I – 1). c) Find a conserved quantity in terms of the dimansionless variables in (b). d) Show that the model predicts cycles in the population of both species for almost all initial conditions.
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