% Integrate the Moore-Spiegal equations. % Moore, D.W. and E. A. Spiegel, 1966, A thermally excited nonlinear % oscillator, Journal of Astrophysics, 143, 3, 871-887. % System equations: % \dot{x}(1) = x(2) % \dot{x}(2) = x(3) % \dot{x}(3) = -x(3)-(a-b+b*x(1)*x(1))*x(2)-a*x(1); % Written by Jim Hansen, Feb 2003 for 12.990 students % Specify the dimension of the system dim = 3; % Specify the initial conditions x = [1 2 3]; % Specify the parameter values (a, b) par = [26. 100.]; % Specify the integration step size h = 0.01; % Specify the length of integration steps = 2^12; % Integrate the equations over length steps to remove any transient behavior for i=1:steps xout=step_it('derivsms',x,par,h,dim); x=xout; end % Integrate the equations over length steps and record state for plotting for i=1:steps xout=step_it('derivsms',x,par,h,dim); state(i,:)=xout; x=xout; end % Make a pretty picture figure;plot3(state(:,1),state(:,2),state(:,3)'.'); title('The Moore-Spiegal attractor'); xlabel('x');ylabel('y');zlabel('z'); print -djpeg90 ms.jpg