# Three variables bifurcation diagram

I'm trying to reproduce a paper. The point is that I have three variables and I will like to do the bifurcation diagram.The paper is this one:"A chaotic model of migraine headache considering the dynamical transitions of this cyclic disease" by Atiyeh Bayani, Sajad Jafari,Boshra Hatef and Julien Clinton.If you want to check it all. I'll show you the model in wich all the parameters are fixed except (e01) which is going to be my bifurcation parameter.Any idea?

A1dot[A1_, e01_, A2_,
A3_] := ((e01 + c1*A1)*
s1 + (K11*A1 + K12*A2 + K13*A3)*
q1*((e01 + c1*A1)^
p1/((e01 + c1*A1)^
p1) + ecrit1^p1))*(1 - A1) - (d1*A1);
A2dot[A1_, A2_,
A3_] := ((e02 + c2*A2)*
s2 + (K12*A1 + K22*A2 + K23*A3)*
q2*((e02 + c2*A2)^
p2/((e02 + c2*A2)^
p2) + ecrit2^p2))*(1 - A2) - (d2*A2);
A3dot[A1_, A2_,
A3_] := ((e03 + c3*A3)*
s3 + (K31*A1 + K32*A2 + K33*A3)*
q3*((e03 + c3*A3)^
p3/((e03 + c3*A3)^
p3) + ecrit3^p3))*(1 - A3) - (d3*A3);

• Please edit your question to include the Mathematica code for the equations. Also include any constraints/assumptions for the parameters/variables. Jul 16, 2019 at 0:28
• "all the parameters are fixed except (e01)" -- Edit the question to include the specific fixed values of the parameters. Jul 16, 2019 at 1:27
• I'm sorry!. I totally forgot to write the values of the parameters. For the other side, I'm not completely sure about the constraints, probably you could look at the section "Numerical results and discussion" on the paper because I'm a little bit lost with their procedure and I can't find an explicit constraint. Just the values of A [0,1] and all the parameters values. Jul 16, 2019 at 2:14
• c1 = 1; s1 = 0.1; K11 = 0; K12 = -1; K13 = -7; q1 = 1; p1 = 4; ecrit1 = 1; d1 = 0.1; e02 = 1; c2 = 1; s2 = 0.1; K21 = 0; K22 = -1; K23 = -7; q2 = 1; p2 = 4; ecrit2 = 1; d2 = 0.1; e03 = 1; c3 = 1; s3 = 0.1; K31 = 0; K32 = -1; K33 = -7; q3 = 1; p3 = 4; ecrit3 = 1; d3 = 0.1; Jul 16, 2019 at 2:18
• Could you please add the equations in Mathematica form? Jul 16, 2019 at 6:43