psheet5 - * a the natural growth rate of rabbits in the...

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Data Analysis Modelling and Simulation MATH1711 Epiphany Term Practical Sheet 5 Aim : To investigate a relevant system of discrete nonlinear equa- tions, namely the Lotka-Volterra or Predator-Prey model R n +1 = R n + aR n - bR n F n F n +1 = F n - cF n + dR n F n by changing the parameters and observing the outcome. The two equations above are a discrete four parameter model describing the interaction between two species in an ecosystem. For sake of description, imagine a colony of rabbits ( R n in the n ’th year) with a plentiful food supply and a colony of foxes ( F n in the n ’th year) which eat the rabbits. The parameters a, b, c, d > 0 represent:
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Unformatted text preview: * a the natural growth rate of rabbits in the absence of predators; * b the death rate of rabbits due to predation (the number of encounters between foxes and rabbits is assumed to be propor-tional to the both the number of rabbits and foxes); * c the natural death rate of the foxes in the absence of food; * d the rate of increase of foxes due to encounters with the rab-bits. Before you visit the AiM server, how do you think the populations of rabbits and foxes will fare in the course of time talk it over with your neighbour or tutor?-...
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This note was uploaded on 02/04/2011 for the course MATH 1711 taught by Professor Dru.picchini during the Spring '11 term at Durham.

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