# ODEs system

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Andrea on 26 Jul 2011
i'm trying to solve this system of differential equations, can someone told me how to use the ODE45 function?
dPp/dz= Pp*gammap*(sigmape*N2 −sigmapa*N1)−α*Pp;
dPs/dz= Ps*gammas*(sigmase*N2 −sigmasa*N1)−α*Ps:
dPASE/dz=PASE*gammas*(sigmaSE*N2-sigmasa*N1)+2*sigmase*h*gammas*Vs*Δv-alfas*PASE;
with N1=ρ*(1+W12*t)/(1+(W12+W21)*t+R*t)
N2=ρ*(R*t+W21*t)/(1+(W12+W21)*t+R*t)
W12=[(sigmasa*gammas) / (h*Vs*A)](Ps+PASE) W21=[(sigmase*gammas) / (h*Vs*A)](Ps+PASE) R=[(Pp*gammap*sigmapa) / (h*Vp*A)](Ps+PASE)
(gammap,gammas,sigmase,sigmape,sigmapa,sigmasa,h,Vs,Vp,A,Δv,α,ρ are known parameters).

Arnaud Miege on 29 Jul 2011
Also, there seems to be 4 variables, not three. Below is the modified code I used and the results I get with your parameters. Again, check the values and the units.
Pp=y(1);
Ps=y(2);
PASE_plus=y(3);
PASE_minus=y(4);
W12=(((sigmasa*gammas)/(h*Vs*A))*(Ps+PASE_plus+PASE_minus));
W21=(((sigmase*gammas)/(h*Vs*A))*(Ps+PASE_plus+PASE_minus));
R=((Pp*gammap*sigmapa)/(h*Vp*A));
N1=(rho*((1+W21*t)/(1+(W12+W21)*t+R*t)));
N2=(rho*((R*t+W12*t)/(1+(W12+W21)*t+R*t)));
dydz(1)=Pp*gammap*(sigmape*N2-sigmapa*N1)-alfap*Pp;
dydz(2)=Ps*gammas*(sigmase*N2-sigmasa*N1)-alfas*Ps;
dydz(3)=PASE_plus*gammas*(sigmase*N2- ... sigmasa*N1)+2*sigmase*N2*gammas*h*Vs*deltav-alfas*PASE_plus;
dydz(4)=-PASE_minus*gammas*(sigmase*N2- ... sigmasa*N1)+2*sigmase*N2*gammas*h*Vs*deltav+alfas*PASE_minus;
And this is how I call the|ode| solver:
[z,y]=ode45('signalFW',[0 20],[10 0.001 0 0]);
figure(1),subplot(2,1,1),plot(z,y(:,1:2)),grid on,ylabel('Power in mW'),legend('Pp','Ps');
subplot(2,1,2),plot(z,y(:,3:4)),grid on,xlabel('length EDFA in m'),ylabel('Power in mW'),legend('PASE+','PASE-');
This gives me the following results:
Is that what you'd expect? If not, check the values of your parameters.
Arnaud
##### 1 CommentShowHide None
Andrea on 29 Jul 2011
Your results are the same as mine..maybe there is something wrong with the parameters. Thank you!

### More Answers (2)

Arnaud Miege on 27 Jul 2011
Have a look at the examples provided in the documentation. You need to write a function that computes the derivatives of your variables as a function of time and the variables themselves, and pass this to the ode solver.
HTH,
Arnaud
Arnaud Miege on 29 Jul 2011
Can you just upload an image of the equations and the results you expect for certain numerical parameters?

Arnaud Miege on 29 Jul 2011
This is the results I get with your code:
##### 2 CommentsShowHide 1 older comment
Arnaud Miege on 29 Jul 2011
The code looks correct if you refer to equations (1) to (9) of the paper. However, you should check that the units used for the various parameters are consistent, and that the numerical values make sense.