MATLAB: How to Find the period of a periodic function

ordinary differential equationsperiodperiod of periodic signalset of equations

How do I find the period of this function?
*Note y(1) is equivalent to x and y(2) is equivalent to y in this set of equations.
My code:
sym vars
a=1; b=1; c=0.1; d=0.1;
RHS=@(t,y)([a*y(1)-b*y(1)*y(2); c*y(1)*y(2)-d*y(2)]);
[t,y]=ode45(RHS, [0 100], [5,0.2]);
figure
plot(t, y(:,1))
xlabel('t (in years)'); ylabel('Number of Prey (in millions)');
title('Number of Prey for 100 Year Period');
legend('x vs t');
set(gca, 'fontsize', 16);

Best Answer

Use the Signal Processing Toolbox findpeaks function: 
a=1; b=1; c=0.1; d=0.1;
 
RHS=@(t,y)([a*y(1)-b*y(1)*y(2); c*y(1)*y(2)-d*y(2)]);
[t,y]=ode45(RHS, [0 100], [5,0.2]);
figure
plot(t, y(:,1))
xlabel('t (in years)'); ylabel('Number of Prey (in millions)');
title('Number of Prey for 100 Year Period');
legend('x vs t');
set(gca, 'fontsize', 16);
[pks,locs] = findpeaks(y(:,1));                                     % Peaks & Locations
mean_period = mean(diff(t(locs)));                                  % Period
text(min(xlim)+0.1*diff(xlim), min(ylim)+0.95*diff(ylim), sprintf('Mean Period = %.2f time units', mean_period))
.
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