Qualitative Analysis: Answer to Example3
Example: Consider the first order system
- Graph the nullclines for this system.
- Insert direction field "arrows" at the nullclines
- Determine the general direction of the direction field in each of the regions cut out by the nullclines.
- Sketch possible phase portraits for the two initial conditions indicated by "dots" for as long as the phase portraits stay within the graph's frame.
- Find all the equilibrium points of the system.
- The x-nullclines can be obtained by setting x'=0, i.e.
The y-nullclines can be obtained by setting y'=0, i.e.
- For 2, 3, 4, use the following graph:
- The equilibrium points of the system are the intersection points
of the x-nullclines and y-nullclines. Therefore,
which yields x=2 and . Hence, we have two equilibrium points
[First Order D.E.]
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