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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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