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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

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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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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