Ikeda Bifurcation

 

 

Ikeda Attractor

 

Instructions:
Applet draws Ikeda bifurcation (U,X) for different values of 0.3 < U < 1.0 parameter. System is conservative for U = 1, for lower values of U system is dissipative.
You can enlarge a fragment of attractor by dragging a rectangle with mouse. Applet will redrawn rectangle automatically.
Cycles is the cycles number that is made before poits are plotted. They are used to stablize solution. MaxIter is number of points that are plotted.
Description:
Ikeda attractor is generated by transforamtion:
Z -> A + B.Z.exp{i[0.4 - 6/(1 + 2Z.2Z)]}
Z = X + iY
or using real variables:
 Xn+1 = 1 + U(Xncos(t) - Ynsin(t))
Yn+1 = U(Xnsin(t) + Yncos(t))
t = 0.4 - 6.0/(1 + Xn2 + Yn2)

You can also analyse attractor and Lapunov exponents for above transformations.

 

Ikeda attractor

Lapunov exponents for Ikeda



back


back to main page