(adsbygoogle = window.adsbygoogle || []).push({}); 1. Given Information/Objectives

The following system for "stable competition":

dx/dt=(2-2x-y)x

dy/dt=(2-x-2y)y

Find the equilibrium points for the system.

Using the Jacobian matrix, linearize the system about the equilibrium that has both species present.

Classify this equilibrium.

Plot direction field and orbits.

2. The attempt at a solution

After finding equilibrium points (2/3,2/3), and the Jacobian (provided that the equilibrium points I found were correct) for the previously mentioned points (J[2/3,2/3]=28/9). I don't know where to go from here; how do I know what kind of equilibrium it is??

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# Systems of Differential Equations- Two models of interacting species

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