Homework 1
Problem 1
Consider Lotka-Volterra predator-prey model,
dx
= ax + bxy
dt
dy
= cy + dxy
dt
with the prey and predator population data given at
http : //www.math.tamu.edu/ ∼ yalchin.ef endiev/math442 spring04/homework page.html
(the data for 50 years, 1900-1950, i.e., x(0), . . . , x(50) for prey and y(0), . . . , y(50) for predator
data).
1) Write a MATLAB routine for calculating a, b, c, d 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.
2) Write MATLAB routine (*.m file) that solves Lotka-Volterra equation with prescribed
a, b, c, d 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.
3) Write MATLAB routine ( *.m file) which does both part 1) and 2) when executed.
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