Recent content by dr29

Yes sorry, it is an equilibrium, but it is never reached in the case I'm interested in. Let me be more explicit: I'm looking for a steady-state solution for the pair of PDEs: dx/dt=(a-b y)x(1-x)+d^2 x/dz^2 dy/dt=(a-b x)y(1-y)+d^2 y/dz^2 The initial condition (at time t=0) is x=y=0 everywhere...

OK thanks for your help! Unfortunately x and y don't reach a/b at the same time, as can be seen in this new figure with a=0.05, b=0.2 (so a/b=0.25). So with this solution, I have the equilibria (x,y,u,v)=(1,0,0,0), (x,y,u,v)=(0,1,0,0), but not (a/b, a/b, 0,0)... What would be great would be...

Thank you for your response! Sorry I should have been more specific; the parameters satisfy 0<a<b<1; attached is the form of the solution I'm looking for (with x/y in blue/red). Here the variable is set at 0 when x=y. Even if there's no simple solution, the value of x=y at 0, and the slopes at...

Hello, I have a system of two second-order autonomous ODEs arising from a population genetics model: (a-b y)x(1-x) + x''=0 (a-b x)y(1-y) + y''=0 where a and b are constants, and x, y are fonctions of t. Is there any hope to solve this system? Thank you for your help.