Math 5110/6830
Instructor: Alla Borisyuk
Homework 7.2
Due: October 27
1. In the general two species interactions model that we considered in class:
x_ = x + xy
y_ = y + xy
analyze the following cases:
a) Mutualism of two species that cannot survive alone
b) A competition model in which one of the populations is self-sustainable and
the other is not.
In each case I want to see nullclines with representative arrows on and between nullclines; xed points and their stability analysis via linearization; phase
space (probably on a separte graph)that clearly shows representative trejectories in the phase space; a description, in words, for what will happen with either
population when they start at dierent initial conditions.
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