## Bifurcation diagram for autonomous ODEs...

Hello,

I would like to study the period doubling bifurcation behaviors of autonomous ODEs.

Although I know how to plot the Poincare section and bifurcation diagram for non-autonomous ODEs, such as Duffing oscillator, I totally stuck at the autonomous ones. Could you please help me.

It could be greatly helpful if you could share me the code of bifurcation diagram for, say, Rossler or Lorenz systems?

Very kind wishes,

Wang Zhe

## How to draw state machines?...

Is there a library to draw state machine diagram from logic table in Maple?

## I have problem to plot this equation!...

Hi

I have problem to plot(2D)  some equations that have 3 variables (to obtain one diagram with some curve ).

like this equation

ln(2*s*t+2*s*x*sqrt(t)/sqrt(pi)+x^2)-2*s*(arctan((s+x*sqrt(pi/t))/sqrt(2*pi*s-s^2))-(1/2)*pi)/sqrt(2*pi*s-s^2) = 0

I should plot x v.s t for s=0.01,0.005,0.003,0.002

please  help me to understand how can plot like these equation.

thanks

## FeynmanDiagrams...

I remember to have seen and used a command to make the graph of the output of FeynmanDiagrams but I can not find more sample files. Someone can tell me how to do (plot a Feynman graph using the result of FeynmanDiagrams).

Thanks and sorry for my english.

## what is characteristic of adjacency matrix of all ...

want to write in maple code

to generate all commutative diagram

however, i only know a -> b, b-> c , a->d , d-> c

another problem is

would like to enrich theory , however, do not know how to connect property such as equations with diagram

## bifurcation diagram...

How would i label the axis and change its font and size.

Also, how would i move the horizontal axis down, so that the whole diagram can be seen. (Hope that makes sence)

Finally, there are some odd points between 0 and 1 on the vertical axis, how do you get rid of these...

Digits:=20: N:=10000: M:=100: x_max:=1: r_min:=0:
r_max:=4: for n from 0 to N do r:=r_min+n/N*(r_max-r_min):
x:=evalf(x_max*rand()/10^12):for m from 0 to M do x:=x*exp(r*(1 - x)): od:
X[n]:=x: od:
with(plots):
bifpoint:={seq([r_min+j/N*(r_max-r_min),X[j]],j=0..N)}:
pitchf:=pointplot(bifpoint,symbol=point):display(pitchf);

Thanks

## Maple - Bifurcations...

I have the command;

> restart: Digits:=20: N:=10000: M:=100: x_max:=1: r_min:=2.5:
> r_max:=4: for n from 0 to N do r:=r_min+n/N*(r_max-r_min):
> x:=evalf(x_max*rand()/10^12):for m from 0 to M do x:=r*x*(1-x): od:
> X[n]:=x: od:
> with(plots):
> bifpoint:=[seq([r_min+j/N*(r_max-r_min),X[j]],j=0..N)]:
> pitchf:=pointplot(bifpoint,symbol=point):display(pitchf);

This plots the bifurcation diagram for the logistic model f(x) = r*x*(1-x).

How do i plot the bifurcation diagram for f(x) = r*(8 - 2*x^2).

I've tried just replacing the function but it does not work.

## Rossler system, initial investigation

by: Maple

Here is the Rossler system, one of the simplest examples of 3 dimensional deterministic chaos (under certain conditions according to "params"). Thanks to Doug and Joe for various assists. Comments and critiques most welcome !

restart;
interface(displayprecision=10):
ross_x:=diff(x(t),t)=-y(t)-z(t):
ross_y:=diff(y(t),t)=x(t)+a*y(t):
ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t):
rossler_sys:=ross_x,ross_y,ross_z;

#Find fixed points:
sol:=solve({rhs(ross_x...

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