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Predator-Prey Models. Pedro Ribeiro de Andrade Gilberto Câmara. Acknowledgments and thanks. Many thanks to the following professors for making slides available on the internet that were reused by us Abdessamad Tridane (ASU) Gleen Ledder (Univ of Nebraska)

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predator prey models

Predator-Prey Models

Pedro Ribeiro de Andrade

Gilberto Câmara

acknowledgments and thanks
Acknowledgments and thanks
  • Many thanks to the following professors for making slides available on the internet that were reused by us
  • Abdessamad Tridane (ASU)
  • Gleen Ledder (Univ of Nebraska)
  • Roger Day (Illinois State University)
hare and lynx populations canada
hare and lynx populations (Canada)

Note regular periodicity, and lag by lynx population peaks just after hare peaks

predator prey systems
The principal cause of death among the prey is being eaten by a predator.

The birth and survival rates of the predators depend on their available food supply—namely, the prey.

Predator-prey systems
predator prey cycles

prey population

increases

prey population

increases

predator population decreases

as less food

predator population increases

as more food

prey population decreases

because of more predators

Predator-prey cycles

normal prey population

generic model
Generic Model
  • f(x) prey growth term
  • g(y) predator mortality term
  • h(x,y) predation term
  • e - prey into predator biomass conversion coefficient
lotka volterra model
Lotka-Volterra Model

r - prey growth rate : Malthus law

m - predator mortality rate : natural mortality

a and b predation coefficients : b=ea

e prey into predator biomass conversion coefficient

predator prey systems2
Suppose that populations of rabbits and wolves are described by the Lotka-Volterra equations with: k = 0.08, a = 0.001, r = 0.02, b = 0.00002

The time t is measured in months.

There are 40 wolfes and 1000 rabbits

Predator-prey systems
equilibrium point
The point (1000, 80) is inside all the solution curves. It corresponds to the equilibrium solution R = 1000, W = 80. Equilibrium point
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