# 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.

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#### 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.