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Topic: Driven van der Pol oscillator (n = 2)
Replies: 11   Last Post: Feb 26, 2013 7:33 AM

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HUYNH

Posts: 1
Registered: 3/12/08
Driven van der Pol oscillator (n = 2)
Posted: Mar 12, 2008 10:11 AM
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How can I solve 2 equations :

dz1/dt = z2
dz2/dt = 5*(1-z1^2)*z2-z1+5*cos(2.47*t)

I can't find any example to solve differential equations
with expression of t ( par example +5*cos(2.47*t) ). My
problem is similar with this Driven van der Pol oscillator
(n=2).

------------------------------------------------------------

My problems is 3 differential equations :

Dy1*c1=k01*(yext-y1)+k12*(y2-y1)
Dy2*c2=k12*(y1-y2)+k23*(y3-y2)
Dy3*c3=k03*(yext-y3)+k23*(y2-y3)

with y1(0)=300,y2(0)=300,y3(0)=300
k01=10, k12=11, k23=12, k30=13
yext=300*sin(2*pi*f*t)
f=1/24

-----------------------------------------------------------

My m-file for the function is :

function [t,y] = m(k01,k12,k23,k30,c1,c2,c3,yext)
tspan = [0 200];
y0 = [0; 3];
[t,y] = ode15s(@v,tspan,y0);

function dydt = v(t,y)
dydt = [ (k01*(yext-y(1))+k12*(y(2)-y(1)))/c1;
(k12*(y(1)-y(2))+k23*(y(3)-y(2)))/c2;
(k23*(y(2)-y(3))+k30*(yext-y(3)))/c3 ]
end

end

-----------------------------------------------------------

My run m-file is :

clear all;
clc;

% les coefficients
c1=2.5e6;
c2=2.5e6;
c3=2.5e6;
k01=10;
k12=11;
k23=12;
k30=13;

% temperature ext
f=1/24;
yext=300*sin(2*pi*f*t);

% solve
[t,y] = m(k01,k12,k23,k30,c1,c2,c3,yext);
plot(t,y(:,1),'-',t,y(:,2),'--',t,y(:,3),'o')
title('Solution of 3 DE');
xlabel('time t');
ylabel('solution y');
legend('y_1','y_2','y_3');

----------------------------------------------------------

Thanks a lots.



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