Exercise 2. (20 points.] The Lorentz Attractor is a well-known example of a chaotic sys- tem,...
Exercise 2. (20 points.] The Lorentz Attractor is a well-known example of a chaotic sys- tem, i.e. a system that can have radically different responses for arbitrarily close initial conditions. Its dynamic equations are = a(32-2) 22 = 26-23) - 12 which can be used to model a two-dimensional flow of liquid warmed from below and cooled from above. To study the system behavior, perform the following: a) Create the MATLAB function dx-Lorentz(x, a, b, c) to compute the derivative d'; b) Given a = 10,6 = 28, c = 8/3, and Xo = 11; 1; 1), write a for loop that performs the following iterations 5 times, • Generates Ax as a 3 x 1 vector of uniformly distributed numbers belonging to the interval (-10-9, 10-*);