This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: trajectories, estimate the largest Liapunov exponent for the Lorenz system, assuming that the parameters have the values r = 28, σ = 10, b = 8 / 3. You will need to use the 4th-order Runge-Kutta integrator ode.m on the course website, since the matlab integrators like ode45 do not use a uniform time-step. Type [ y1 , t ] = ode(D, y0 , t0 , tf , Ns , ord, fig) ; with your chosen initial vector y0 to create a solution matrix y1 . Make sure that your initial vector is on the attractor! Repeat with another nearby initial vector to create a second solution matrix y2 . Type dy = y2-y1 ; to create the diﬀerence. Either of the commands nn = sum(abs(dy)’ )’ ; or nn = sqrt(sum(dy’ .* dy’ ))’ ; will create a column vector of norms of the diﬀerences for all times. Then plot(t, log(nn)) ; will plot the logarithm of the norm versus time, and polyfit(t, log(nn), 1) ; will give the slope and intercept of the best linear ﬁt....
View Full Document