1. The problem statement, all variables and given/known data Consider the system of equations : x' = x-y-x^3 and y'=x+y-y^3 a) Draw a phase plot ( Done numericlly program listed here in matlab) b) Prove analytically that at-least one stable cycle exists ( Used Poincare Bendixon theorem to prove done) c) Compute the period of the cycle numerically ( No idea about this >>) 2. Relevant equations Limitcycle.m clc; clear all; options=; timeperiod=; phasepoints=; xnew =0.01; ynew =0.01; % x_start= -0.9:0.1:0.9; % xstart = 0.9:-0.1:-0.9; % x_start= [x_start,xstart]; % y_start= -0.9:0.1:0.9; % ystart= -0.9:0.1:0.9; % y_start=[y_start,ystart]; %for u=1:size(x_start,2) [t y]=ode23('cyclefunc',[0 50],[xnew ynew],options); timeperiod=[timeperiod;t]; phasepoints=[phasepoints;y]; %end n=0.015; points=y; figure(2) plot(phasepoints(:,1),phasepoints(:,2)); xlabel('X-axis'); ylabel('Y-axis'); % plot3(t,y(:,1),y(:,2)); % xlabel('Time'); % ylabel('Y-axis'); % zlabel('X-axis'); % startingNode=y(4,:); % filename: cyclefunc.m function dydt = f(t,y,flag) dydt = [y(1)-y(2)-y(1)^3; y(1)+y(2)-y(2)^3]; plot(y(1),y(2)); xlabel('X-axis'); ylabel('Y-axis'); drawnow; hold on; axis([-1.3 1.3 -1.3 1.3]); These programs generate the limit cycle numerically and it is correct 3. The attempt at a solution Now the attempt is the above program itself. I scoured the internet to search for an algorithm for generating time period numerically . I saw some programs like pplane which do it for you ( I doesnt show how it calculate though) Any one can tell me a primitive algorithm for calculating this ?? Or if my current matlab program can be modified to calculate the same ?