This project aims to study logistic growth from its classical origin as a tool to study population dynamics.

For your given data set

Year	Grey Wolves (Montana)
1999	75
2000	95
2001	125
2002	180
2003	180
2004	155
2005	255
2006	320
2007	425
2008	495
2009	525
2010	570
2011	655
2012	625
2013	625
2014	555

, do the following:

1) Assuming logistic growth, determine appropriate values for K, the carrying capacity, and r, the intrinsic growth rate, based on your data set. Describe your approach and process for each in detail and provide all relevant work.

2) State your logistic model (the Verhulst DE) with the constants determined from the question above. Define all quantities and parameters and describe their units. You should ensure that the units on each side of the DE match. State and justify an initial condition as well. Next, you are to incorporate a harvesting term, E, that is proportional to the population size. Write a modified model incorporating this new, harvesting term. For more details, look up the Gordon-Schaefer model. Note: Do not solve the original model or the modified model. Only setup and description are required for each of them.

3) In your own words, describe what harvesting means within the context of this scenario. State why and when harvesting would occur or be needed.

4) Plot the phase line for the Gordon-Schaefer model and discuss the stability of its equilibrium points as a function of the harvesting coefficient. Determine if there is a bifurcation point at any value(s) of E. Provide all relevant work. (it wants this to be done on MATLAB

5) Choose an appropriate numerical method (Improved Euler or Runge-Katta) and implement it in MATLAB to solve the given model. Choose a very small step size to guarantee a very precise numerical solution. Leave the harvesting coefficient as an arbitrary parameter, E. Using your MATLAB code, plot different solutions on the same figure that shows how different values of the harvesting coefficient lead to different outcomes for the grey wolf population. Include the MATLAB plot and your code with your submission.

any help on this assignment would be greatly appreciated. also, please do not answer this question unless you also can give a MATLAB code as that is the part I am mostly in need of help for