Discrete logistic model

We are going to re-visit the process of building and analyzing the model for the growth of the Paramecium Aurelia in isolation with the constant level of nutrients.

Load the data from the data file. Plot the data

Remember that the future population level is the current level from change. Open a new figure and plot the change from day to day as a function of time. Why do you think it has this shape?

Plot the change again, in the new figure, but this time as a function of the current population size. We are going to approximate the change by k(N-pn)pn. Do you think this is a good approxmation with k=0.00145 and N=540?

Now the full model is p_{n+1}=p_n+k(N-p_n)p_n. Simulate the model and compare your results with the data by plotting it on the same figure as the original data.
What are the steady states and their stability?