Hello,
I study laser physics, using "Laser Physics" by Eberly and Milloni. I am confused regarding the notion of gain and the saturation effect. According to the book, the gain is defined as
## g(v) = \dfrac{g_o(v)}{1+I_v/I^{sat}_{v}} ##
where ## I^{sat}_{v}## is the saturation intensity and...
Hello guys
I struggle since yesterday with the following problem
I am reading the book "Elements of applied bifurcation theory" by Kuznetsov . At one point he has the following Taylor expansion of a nonlinear system with respect to x=0 where ##x\in \mathbb(R)^n##
$$\dot{x} = f(x) = \Lambda x +...
Yes, I think you are right. Solving the set of ODEs with a stiff solver in Matlab, it seems that the ## P_{gs}## reaches the value 0.5 sooner than the other variables reach their steady state. The problem is that I cannot ommit the ODE associated with the ##P_{gs}## variable. In order to create...
Yes but we now use the values ##E^n_{real}=0.6815 ##, ##E^n_{imag}=-0.4789 ##. So this term now is
$$ -1.9514*10^{-10}*2*((E^n_{real}*10^{18})^2+(E^n_{imag}*10^{18})^2)+\ldots$$
The exponent 26 is there again. 18+18-10=36-10=26.
Ok, I fixed my mistakes. Now we get the same matrix except from the second row. How did you compute it ?
Edit: I see. There is a second mistake. Oh my god. If only I wasn't so hasty with my math.
In my code, I replaced all the Ereal, Eimag terms with 1e18*Ereal, 1e18*Ereal. After that, I computed the Jacobian Matrix ( which up to this point is wrong) and then I divided every element in the last two rows by 1e18. What have I done wrong ?
Pwl=0.271205495697359;
Pgs=0.500000000000001...
First of all let me tell you how I scaled my matrix. Let's write the equations this way
$$ \dfrac{dP_{wl}}{dt}=F_{wl}(P_{wl},P_{gs},P_{es},E_{real},E_{imag})\\
\dfrac{dP_{gs}}{dt}=F_{gs}(P_{wl},P_{gs},P_{es},E_{real},E_{imag})\\...
Thank you very much for your response. My set of equations is
$$
\dfrac{dP_{wl}}{dt}= 5.8858*10^8+2.2071*10^8*P_{es}-4.0833*10^{9}*P_{wl}+1.8625*10^9*P_{es}*P_{wl} \\
\dfrac{dP_{gs}}{dt}=...
Hello guys,
I try to use the Newton - Chord technique in order to solve a nonlinear system and find it's equilibrium points.This method requires the inverse of the Jacobian Matrix of the nonlinear system. After the linearization around the given starting point x0, I create a linear...
Hello my friends,
I am studying excitability in quantum dot lasers and I see a lot of bifurcation diagrams with saddle node bifurcations, Hopf bifurcations, homoclinic bifurcations, PD bifurcations etc. I know some basic things about non-linear systems but I have never met the notion of...