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For the following equations sketch the bifurcation diagram, determine type of bifurcation, and find the critical value of $r$.

$$\dot{x} = rx + \cosh x$$

I seem to understand how to do the first two parts of the questions ( sketch the bifurcation diagram and determine type of bifurcation). Though I never really understood how to find THE VALUE of "$r$" ....

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Any comments on my reply to your earlier question on bifurcation? – Gerry Myerson Nov 1 '12 at 0:15

A critical value is a value where a bifurcation occurs. Hint: Look at the graph of the equation $r x + \cosh(x) = 0$, and see where the number of critical points changes.

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