MATLAB URGENT HELP NEEDED DUE IN 1 HOUR

PLEASE HELP POSTING TWICE NOW

Task 1 (of 2) 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-11 with 6 t(n) = 0.4 - 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(O) = 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 Amin = -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. Attractors (Test Values): Case a: u = 0.3: Your graph y vs x should be a single dot. This means that as time goes (n increases), the map outputs the same values of x and y. This is a periodic attractor. Place your figure here. Case b: u = 0.5: Your graph y vs x should be two dots. This means that as time goes (n increases), the map will alternate between two values of (x1, y.) and (x2, Yz). This is a bi-periodic attractor. Place your figure here. Case c: u = 0.7: Your graph y vs x should be many "random dots. This means that as time goes (n increases), the map will be unpredictable or chaotic. This is called a chaotic attractor. Place your figure here. Case d: 4 = 0.9: Your graph y vs x should be many "random dots. This means that as time goes (n increases), the map will be unpredictable or chaotic. This is called a chaotic attractor. The chaos index here is said to be higher. Place your figure here