Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » Software » comp.soft-sys.math.mathematica

Topic: DE system (Phase Plane)
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Larry Smith

Posts: 5
Registered: 12/7/04
DE system (Phase Plane)
Posted: Mar 11, 1997 1:39 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

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.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.