Question
Transcribed Text
Problem 1: Consider the system
dx = - x - ß123
dt
dy =
dt
k2
where all parameters are positive. Analyze completely this system. You will find 4 different phase
portraits based on the parameter values.
Problem 2 (Hard): Consider the following system
dy dt =
with
x
for
Show that the four equilibrium points are [x3,9(x3)] where x2,23 =
1)
V (B-1)2-1. - a There are 6 regions of parameter space that correspond to various phase
portraits. Find the conditions for each and draw only the phase portraits with null clines for all 6.
Pick one to draw the complete phase portrait.
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