Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

What are the fixed points of

$$ θ'=1-a\sinθ $$

$$\text{what type of bifurcation occurs at } a=1, \;\;\;θ=π/2 $$


$$ 1/a=\sinθ \text{ or } θ=\arcsin(1/a) $$

I cant seem to find the proper fixed points after this step

share|cite|improve this question

You don't need to find any fixed points analytically to get the answer you are seeking.

Plot the function $$ a=\frac{1}{\sin \theta} $$ in the interval $(\pi/2-\varepsilon,\pi/2+\varepsilon)$. Fixing $a=\hat{a}$ gets you an idea about the number of fixed points and their types (this is called bifurcation diagram).

Note that if $a>1$ then you have two fixed points, one is stable and another is unstable. If $a<1$ then you have no fixed points, the two above approached each other and collapsed. This should be known to you as a saddle-node, or tangent, or fold bifurcation.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.