1
$\begingroup$

Suppose, I have a system of simultaneous nonlinear differential equations as follows:

x'=x-x^3-x*y^2-a*x+h
y'=y-y^3-y*x^2+a*y

where, x & y are variable ; x' & y' represents time derivative of x and y ; a & h are parameters.

Now to solve this, one can use DSolve or by taking x'=0 & y'=0 (for fixed point calculation) , i.e. take the polynomial and by using FindRoot or Ruduce or other options.

My quarry is that what is the easiest way to get fixed points (solutions) in terms of a & h .

$\endgroup$
  • $\begingroup$ Could use In[14]:= Solve[{x - x^3 - x*y^2 - a*x + h, y - y^3 - y*x^2 + a*y} == 0, {x, y}, Cubics -> False] to get parametrized solutions, some using Root objects. They evaluate numerically when given values for the parameters. $\endgroup$ – Daniel Lichtblau Oct 22 '17 at 17:02
1
$\begingroup$

In this case, you can obtain the fixed points with Solve:

Solve[{x - x^3 - x*y^2 - a*x + h == 0, y - y^3 - y*x^2 + a*y == 0}, {x, y}]

However, this will not work in general.

$\endgroup$
  • $\begingroup$ then for general purpose what command should I use @Henrik $\endgroup$ – Bapi Saha Oct 22 '17 at 17:27
  • $\begingroup$ FindRoot. But you can use a long-time solution from NDSolve as starting value. $\endgroup$ – Henrik Schumacher Oct 22 '17 at 17:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.