System of differential equations with periodic function in each equation

Hi, I was wondering if anyone could help explain why I am getting following plot

instead of something which looks more like this

Clearly I have more oscillations than expected.

I have the following two Matlab scripts:

function f=crimp(t,y,g1,g2,l1,l2,om,K1,K2)
f=zeros(3,1);


f(1)=g1-K1*y(1)*(((1+sin((pi*t)/6))/10)+y(3));
f(2)=g2-K2*y(2)*(((1+sin((pi*t)/6))/10)+y(3));
f(3)=(l1*y(1)+l2*y(2))*(((1+sin((pi*t)/6))/10)+y(3))-om*y(3);

and

g1=0.02;
g2=0.01;
K1=1;
K2=1;
l1=0.7;
l2=0.2;
om=0.2;
K=K2/K1;
A=1/10;

inp1=(K*g1)/(A*K+K*g1+g2);
inp2=g2/(A*K+K*g1+g2);
inB=(K*g1+g2)/K;

y0=[inp1 inp2 inB];


[t,y]=ode15s(@(t,y) crimp(t,y,g1,g2,l1,l2,om,K1,K2),[0 60],y0);
hold off
axis([0 60 0 0.25])
plot(t,y(:,1),'-blue',t,y(:,2),'-red',t,y(:,3),'-green')

I don't know where I am going wrong. I have tried to put in dots before operators in the differential equations f(1), f(2) and f(3).

Please can anyone help?

Thanks in advance

Answer 1

[Star Strider]

There are obviously sin calls in ‘crimp’, so that explains the oscillations.

The real question is why you are not getting the decaying exponentials. I suspect the sin calls are actually supposed to be hyperbolic sine calls, using the sinh function instead. When I make that change, the plot comes close to matching the one you want.

The anonymous function version:

crimp = @(t,y,g1,g2,l1,l2,om,K1,K2) [g1-K1*y(1)*(((1+sinh((pi*t)/6))/10)+y(3)); g2-K2*y(2)*(((1+sinh((pi*t)/6))/10)+y(3)); (l1*y(1)+l2*y(2))*(((1+sinh((pi*t)/6))/10)+y(3))-om*y(3)];

for convenience.

[Rachel Kirkland]

Thank you!

I am trying to replicate the results found in a paper; perhaps there was a mistype in said paper.

Thanks for your help, much appreciated

[Star Strider]

As always, my pleasure!

Errors in published papers are much more common than usually realised. I suspect many of have encountered irreproducable results.