Recent content by Aldo Leal

I have the code which solves the Sel'kov reaction-diffusion in MATLAB with a Crank-Nicholson scheme. I would love to modify or write a 2D Crank-Nicolson scheme which solves the equations: ##u_t = D_u(u_{xx}+u_{yy})-u+a*v+u^2*v## ##v_y = D_v(v_{xx}+v_{yy}) +b-av-u^2v## Where ##D_u, D_v## are...

Your definition is totally correct, the missedpoint is that the trapping region must contain the fixed point, especifcically for this system we got $$(b,1/b)$$ as a fixed point, which in other words is the intersection between de isoclines. Now we can se a kind of a "triangle" that take inside...

It is a part of my thesis investigation but I can't figure it out a trapping region

But the fixed point is in the positive half-plane actually now you can see this pictures I'll post it here and you'll see that there is a limit cycle in the positive half-plane, more specific, in the first quadrant so... I need to build a trapping region in order to... at least in averge the...

It's just that I've finding a optimal $$b*=0.900316$$ and $$b=1$$, i.e, $$b\in(0.009316,1)$$ for the values of $$b$$. Now I've to proove a trapping region for those values of $$b$$. I've been analyzing the eigenvalues using the Hopf Bifurcation theory but I can't catch that trapping (attraction)...

But... the isoclines just for themselves doesn't give a trapping region. I mean, if you plot the phase plane you'll see that there are a part where all the vectors go to infinity in the y axis, so it is impossible to take the y-axis as a part of the trapping region. What a can't understand is...

I need to find a trapping region for the next nonlinear ODE system $u'=-u+v*u^2$ $v'=b-v*u^2$ for $b>0$. What theory i need to use or which code in Mathematica o Matlab could help me to find the optimal trapping region.