HOMEWORK 2B - HOMEWORK 2B Due Friday,July10,2015,11:59pm 1...

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HOMEWORK 2B Due: Friday,July10,2015,11:59pm 1. Write a MATLAB script that computes the population of three species under competition. In the class, the predator-prey problem of paramecium and yeast was explored. Now, consider the interaction between three groups of imaginary creatures of X, Y and Z competing for the same food. The populations of these three species are governed by the following Lotka Volterra equations: dx dt = 3x±1− x 10± −2xy −1.5xz,d y dt = 2y±1− y 10± −1.5xy −2yz,d z dt = 2.5z±1− z 10± −2xz −1.5yz, (1) where x, y, z are the population (per unit area) of species X, Y and Z. Note that there are additional quadratic terms and different signs compared with the predator-prey equations mentioned in class. (a) Before you start programming (seriously, just turn the computer off now), write down the discretized governing equations using the forward Euler method in this problem. Use subscripts k and k + 1 to denote the known values at step k and the values to be determined at step k + 1.
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