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Phyrrus
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1. Homework Statement [/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.
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
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.
Homework Equations
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