Can anyone guide me on how to obtain the Hopf Bifurcation diagram? I am very new to this topic.I am trying to plot a Hopf bifurcation diagram for the system with bifurcation parameter α with the following given values:

α = 2.438571114; β = 0.2; δ = 2.3; γ = 0.7; 

My system is

{x'[t] == x[t](1 - x[t]) + x[t]y[t], 
 y'[t] == y[t](δ - (β y[t])/x[t]) - (α y[t])/(γ + y[t])}

Can anyone guide me on how to obtain a Hopf bifurcation diagram. Plot should have parameter α on x-axis and xy on y-axis


closed as unclear what you're asking by anderstood, m_goldberg, Coolwater, José Antonio Díaz Navas, C. E. Mar 26 '18 at 10:07

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Can you give parameter values where there is a limit cycle to get started with? The parameters given result in a blowup.

α = 2.438571114; β = 0.2; δ = 2.3; γ = 0.7;
tmax = 100;

sol = NDSolve[{x'[t] == x[t] (1 - x[t]) + x[t] y[t], 
  y'[t] == y[t] (δ - (β y[t])/x[t]) - (α y[t])/(γ + y[t]),
  x[0] == 1, y[0] == 1}, {x, y}, {t, 0, tmax}][[1]];

(* NDSolve::nderr: Error test failure at t == 15.34966818880772`;
  unable to continue. *)

Plot[Evaluate[{x[t], y[t]} /. sol], {t, 0, 15.349}]

Mathematica graphics


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