Week 8: Advanced Exercises
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Advanced exercises are designed for advanced learners that are ready to take on extra challenges. These exercises are made accessible to all after the class. Note that these exercises typically require more knowledge than what was presented in class.  

.. .. warning :: Training wheels off! The material in today's class is not enough /to solve this problem. 

Adv Exercise: Predator-prey relationship
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.. [-]Elaborate on similarity with SIR model, though now modelling two! Diff eqns
.. [ ]Provide eqn and scenario, tell to model and see how the equilibrium between prey-predator work out. Need to find numbers for this.

The prey-predator relationship was mentioned in this week's module. Using similar structure as the code in this week's regular exercises, proceed to model the scenario below:
    * Populations of rabbits and foxes co-exist in the same habitat
    * Implement the prey-predator relationship using the equation on https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations. You will find it very helpful to complete the regular in-class exercise.
    * Use the following constants:
        * alpha = 0.04
        * beta = 0.0005
        * delta = 0.00005
        * gamma = 0.2
    * Explore multiple initial conditions, you should find two steady states!
    .. Numbers came from here
    .. https://www.stolaf.edu//people/mckelvey/envision.dir/lotka-volt.html