Homework 1
Problem 1
Consider Lotka-Volterra predator-prey model,
dx
= ax − bxy
dt
dy
= −ry + cxy
dt
with the prey and predator population data given (see homework web site) (the data for 50
years, 1900-1950, i.e., x(0), . . . , x(50) for prey and y(0), . . . , y(50) for predator data).
Write a MATLAB routine for calculating a, b, r, c using the given data and linear regression. You will need to compute the gradient of the discrete valued function for this purpose.
Either write a short “for” loop to do this or use the command “gradient”. You will need
to save the data and read it in your *.m file. Write MATLAB routine (*.m file) that solves
Lotka-Volterra equation with calculated a, b, r, c and plots the solution of Lotka-Volterra
equation for prey and predator population (separate graphs, please). For each graph, plot
also the experimental data to show how accurate the simple model predicts the data.
Problem 2
Consider predator-prey model with limited source term for prey population. In this case,
dx
= ax − bxy − dx2
dt
dy
= −ry + cxy
dt
where −dx2 (d > 0) describes the fact that the growth of prey population is limited. Calculate all possible equilibrium solutions and determine whether or not these are stable equilibrium points.
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