# Dynamical System Analysis using Mathematica

Hello there,

Let me start from the beginning. I have dynamical system described by two autonomous ODEs (eqn1, eqn2). To find equilibrium points I used NSolve[{eqn1 == 0, eqn2 == 0}, {x, y}] which gave me 5 solutions in a form {{x->2, y->0},{...},...}. I also constructed Jacobian matrix using M={{D[eqn1,x], D[eqn1,y]},{D[eqn2,x],D[eqn2,x]}} which is written with x and y. Next I need to calculate this Jacobian matrix substituting solutions from NSolve function to find its eigenvalues. So I should have 5 matrices with corresponding eigenvalues. How can I achieve this? The problem is to substitute values from the solution to the matrix.

I will appreciate any help.

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I understood how to extract NSolve output. For this purpose you need to write soln=NSolve[...], then to access the solution values of this function x /. soln[[1]], y/.soln[[1]] (this corresponds to the 1st solution)

So next step will be to substitute those values to the matrix written in terms of x and y. Any ideas?

Can you apply this method to your problem?

In[1]:= mat={{x,y},{x+y+1,2x-3}};
sols={{x->1,y->3},{x->2,y->4}};
Map[mat/.#&,sols]

Out[3]=
{{{1, 3},
{5, -1}},

{{2, 4},
{7, 1}}}

Can you apply this method to your problem?

In[1]:= mat={{x,y},{x+y+1,2x-3}};
sols={{x->1,y->3},{x->2,y->4}};
Map[mat/.#&,sols]

Out[3]=
{{{1, 3},
{5, -1}},

{{2, 4},
{7, 1}}}
Thank you. I used quite similar way of doing this.