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Population Dynamics Simulation

Do the following dynamic simulation problem:

1. The following model is proposed to describe population growth in a confined space. The excess of births over natural deaths causes a growth rate of a times the current number of individuals N. Competition for food causes deaths from starvation at a rate of bN^2 . Simulate the population growth assuming:
a. a = 0.05
b. b = 0.00001
c. N = 500 at time t=0

2. Assume in problem 1 that a second species exists in the same space subject to a1=0.04, b1=0.000015, and N1=1,000 at time t=0. However interspecies fighting causes deaths to both species at a rate that is 0.000001 times the product of their numbers (0.000001N(N1) ). Extend the model to plot the population dynamics for both species.

Solution Preview

Please see attachment.

In brief about the solution:

Sheet 1: Q1: Solution to first part.
dN/dt == delta(N)/delta_t = a*N(t) - b*N(t)^2
=> delta(N) == N(t+delta_t) - N(t) = delta_t * (a*N(t) - ...

Solution Summary

A simulation which estimates growth of the population of a species.