Science:Math Exam Resources/Courses/MATH215/December 2013/Question 06 (c)
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Question 06 (c) 

Suppose the interaction between two species ( is the “prey” while is the predator) can be modelled by the autonomous system: (c) If , determine and . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Consider the stability of each critical point and make a prediction based on this. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The only stable equilibrium solution is (1,2), which is a stable spiral. Saddle points and sources are unstable. While little can be done rigorously, our prediction is that with that as . 