Bifurcation of an ODE
$begingroup$
$x' = mu x − sin x$,
where $µin mathbb R$ is a parameter.
- 1) Classify the bifurcation at $mu=1$
- 2) Identify the largest $mu < 1$ for which the system has a bifurcation. What kind of a
bifurcation is it?
So I tried drawing the bifurcation diagram to help and could see that when $mu=1$ then $x=0$ but I don't know how to show it's a saddle node. For the second part, I only found the jacobian but dont know what to do with it.
ordinary-differential-equations bifurcation
edited Dec 20 '18 at 16:29
Kihlaj
4210
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
$endgroup$
add a comment |
$begingroup$
$x' = mu x − sin x$,
where $µin mathbb R$ is a parameter.
- 1) Classify the bifurcation at $mu=1$
- 2) Identify the largest $mu < 1$ for which the system has a bifurcation. What kind of a
bifurcation is it?
So I tried drawing the bifurcation diagram to help and could see that when $mu=1$ then $x=0$ but I don't know how to show it's a saddle node. For the second part, I only found the jacobian but dont know what to do with it.
ordinary-differential-equations bifurcation
edited Dec 20 '18 at 16:29
Kihlaj
4210
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
$endgroup$
add a comment |
$begingroup$
$x' = mu x − sin x$,
where $µin mathbb R$ is a parameter.
- 1) Classify the bifurcation at $mu=1$
- 2) Identify the largest $mu < 1$ for which the system has a bifurcation. What kind of a
bifurcation is it?
So I tried drawing the bifurcation diagram to help and could see that when $mu=1$ then $x=0$ but I don't know how to show it's a saddle node. For the second part, I only found the jacobian but dont know what to do with it.
ordinary-differential-equations bifurcation
edited Dec 20 '18 at 16:29
Kihlaj
4210
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
$endgroup$
$x' = mu x − sin x$,
where $µin mathbb R$ is a parameter.
- 1) Classify the bifurcation at $mu=1$
- 2) Identify the largest $mu < 1$ for which the system has a bifurcation. What kind of a
bifurcation is it?
So I tried drawing the bifurcation diagram to help and could see that when $mu=1$ then $x=0$ but I don't know how to show it's a saddle node. For the second part, I only found the jacobian but dont know what to do with it.
ordinary-differential-equations bifurcation
ordinary-differential-equations bifurcation
edited Dec 20 '18 at 16:29
Kihlaj
4210
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
edited Dec 20 '18 at 16:29
Kihlaj
4210
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
edited Dec 20 '18 at 16:29
Kihlaj
4210
edited Dec 20 '18 at 16:29
Kihlaj
4210
edited Dec 20 '18 at 16:29
Kihlaj
4210
4210
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
asked Dec 20 '18 at 15:31
Vicem0nVicem0n
343
343
add a comment |
add a comment |
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