Modeling the Ikeda Map By: Jonathan Eads

Background & Methods yn+1 = u(xnsintn + yncostn) The Ikeda Map is a model of light going around and across a nonlinear optical resonator. It is often used in a modified form in order to take the saturation effect of nonlinear dielectric medium into account. The attractor of the system changes as the parameter u is varied. The original map is given by the formula:zn+1 = A + BzneiK/(|zn|2+1)+C A 2D real example of the above form is: xn+1 = 1 + u(xncostn – ynsintn) yn+1 = u(xnsintn + yncostn) tn = 0.4 – 6/(1 + x2n + y2n) For this project I set xn & yn to be random using the rand() function. I set u to be a range a numbers from 0.1 to 1 in 0.01 steps. I ran the model for 1,000 iterations.

Ikeda Map 2D

Run my code with: compute_ikeda_trajectory.m Final_modified.m