MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
5th Edition
ISBN: 9781118629864
Author: Amos Gilat
Publisher: WILEY
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Chapter 9, Problem 35P

The sudden outbreak of an insect population can be modeled by the equation

d N d t = R N 1 N C r N 2 N c 2 N 2

The first term relates to the well-known logistic population growth model where N is the number of insects. R is an intrinsic growth rate, and C is the carrying capacity of the local environment. The second term represents the effects of bird predation. Its effect becomes significant when the population reaches a critical size Nc; r is the maximum value that the second term can reach at large values of N.

Solve the differential equation for 0 t 50 days and two growth rates. R = 0.55 and R = 0.58 day-1, and with N(0) = 10,000. The other parameters are C = 104, N = 104, r = 104day-1. Make one plot comparing the two solutions and discuss why this model is called an “outbreak” model.

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MATLAB: An Introduction with Applications

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