Posted: September 13th, 2017

Predator-Prey Model

Paper, Order, or Assignment Requirements

i will upload a file showing the equations: i want to use falcons dy/dt and rabbits dx/dt as the predators and preys.

The system should exhibit a bifurcation, i.e., should exhibit
different qualitative behaviors when the value of one or more coefficients changes. You should use
generalized parameters (i.e., symbols in place of specific numbers) in formulating your model in
order for the behavior of solutions to be dependent on the value of at least one parameter.

“analysis” You do not have to solve the model system outright (indeed, your system
should be complex enough to preclude this). Instead, you should identify and illustrate the different
possible “behaviors” that solutions exhibit. Explain which parameter(s) you are varying to produce
the different results. Perform an equilibrium stability analysis, and use appropriate software to
produce a phase portrait and graphs of the solutions vs. time (your independent variable).

The final report must contain the following sections, in order: (1) an introduction
explaining the topic or real system being modeled, and articulating a question which a mathematical
model can help answer; (2) development of the model, giving the system of differential equations
and explaining what each term, variable, or parameter represents, and the underlying assumptions;
(3) the actual mathematical analysis (see above); (4) a conclusion which interprets the results of the
mathematical analysis in the context of the real system being modeled; and (5) a list of all resources