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Drawing Bifurcation diagrams for a dynamical system

  1. Nov 13, 2012 #1
    1. The problem statement, all variables and given/known data[/b]
    Consider the dynamical system
    [itex]\frac{dx}{dt}[/itex]=[itex]r[/itex][itex]x[/itex]-[itex]\frac{x}{1+x}[/itex]
    where r>0
    Draw the bifurcation diagram for this system.

    2. Relevant equations



    3. The attempt at a solution
    Well fixed points occur at x=0,[itex]\frac{1}{r}[/itex]-1 and x=0 is stable for 0<r<1 and unstable for all r>1
    For the fixed point at [itex]\frac{1}{r}[/itex]-1, however, it is stable when r-r[itex]^{2}[/itex]<0

    So how do I draw the non-zero bifurcation points? Thanks
     
  2. jcsd
  3. Nov 14, 2012 #2
    Well, the bifurcation diagram is a diagram illustrating how the fixed points change as a function of the parameter. So you have two fixed points:

    [tex](0,\frac{1-r}{r})[/tex]

    So those change as a function of r right? Got two until r=1, got one there, then two again when r>1. Can you not just plot those two fixed points as a function of r? You can do that.
     
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