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Topic: DE system (Phase Plane)
Replies: 0

 Larry Smith Posts: 5 Registered: 12/7/04
DE system (Phase Plane)
Posted: Mar 11, 1997 1:39 AM

I'm trying to the solve the following system of differential
equations:

eq (1) dS/dt = (1/10)S-(1/20)SN

eq (2) dN/dt = (1/100)N-(1/100)N^2-(1/100)SN

I want to plot the phase space (phase plane) sol's , I have determined
that the phase plane and N and S have equilibrim points at N=2, and
N+S=1, these divide the graph into three regions, the area above N=2
is labeled region III with N(dot) <0, and S(dot)<0 the region below
N=2 and to the right of N+S=1 and above the S axis is called region II
with N(dot)<0, and S(dot)>0, the region to the left of the line N+S=1
and (0,0) is region I with N(dot)>0, and S(dot)>0.

I want to use Mathematica to show that
1. the lines N=2 and N+S=1 divides the first quadrant into three
regions in which dS/dt and dN/dt have fixed signs as I have stated.
2. show that every solution of S(t),N(t) of (*) which starts in either
region I or region III must eventually enter region II
3. show what every solution S(t),N(t) of (*) which starts in region II
must remain in there for all future time.
4. conclude that based on part 3 that S(t) as it approaches infinity
for all solutions of S(t), N(t) of (*) wich S(t sub o) and N(t sub o)
positive. conclude too that N(t) has a finite limit (< or = to 2) as t
approaches infinity.

LSmith