(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

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

ẋ = rx + cosh(x)

ẋ = x(r - sinh(x))

ẋ = rx - xe^{-x2}

The attempt at a solution

Fixed points satisfy

f'(x) = r + sinh(x) = 0 ⇒ x._{*}= arcsinh(-r) = -arcsinh(r)

f'(x) = r - sinh(x) - xcosh(x) = 0.

f'(x) = r + 2xe.^{-x2}- e^{-x2}= 0

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Bifurcation Diagrams

**Physics Forums | Science Articles, Homework Help, Discussion**