MATLAB only

In physics and mathematics, the Ikeda map is a discrete-time dynamical system first proposed by Kensuke Ikeda as a model of light going around a nonlinear optical resonator (ring cavity containing a nonlinear dielectric medium). The mathematical expression of the Ikeda map is given as: x(n) = 1 + u[x(n 1)cos(t(n 1)) y(n 1)sin(t(n 1))] y(n) = u[x(n 1) sin(t(n 1)) + y(n 1) cos(t(n-1))] with t(n) = 0.4 - 6 1+x(n)2 + y(n) where u is a parameter of the model (between 0 and 1) and n is a positive integer representing the discrete time. Definition 1: In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve. The Ikeda map has periodic and chaotic attractors as u is increased. Definition 2: In the mathematical field of dynamical systems, a system is said to be in a transient state when a process variable or variables have been changed and the system has not yet reached a steady state. The Ikeda map has a transient phase. For this assignment, we will NOT plot the first 2,000 points to ensure that the system has reached a non-transient state. Develop a MATLAB script to do the following: Prompt the user for a value for u between 0 and 1. Make sure the value entered is valid. Once a valid value is entered for u, calculate x(n), y(n), and t(n) for n = 0, 1, 2, ..., 10,000 assuming x(0) = y(0) =t(0) = 0.4. Plot x(2001:10001) on the x-axis and y(2001:10001) on the y-axis as individual points (i.e., don't connect adjacent points with lines which is the default in the plot command). Note: Within your script, scale your axis so that Xmin = -0.5 and Xmax = 2 for the x-axis, and Ymin = -2.5 and ymax = 1 for the y-axis. You should use a markersize (dot) of 10 (or higher) for better visualization