Help in Bifurcation Diagram

Question

I need to plot a bifurcation diagram for the following non-linear systems represented by the next Mathematica code

    With[{Pr = 10, α = 1.181, β = 0.675, v = 0.77, λ = 8/3},
         s = ParametricNDSolveValue[{
            x'[t] == Pr v (y[t] - x[t]),
            y'[t] == R (β/v) x[t] - α y[t] - (β/v) (R - (α v)/β) x[t] z[t],
            z'[t] == α λ (x[t] y[t] - z[t]),
            x[0] == y[0] == 0.8,
            z[0] == 0.92195},
           z[t], {t, 0, T}, {R, T}, MaxSteps -> ∞]]

Answer 1

Just a kickstart to get the equations right (yours are wrong) and an idea of the system dynamics:

With[{Pr = 10, a = 1.181, b = 0.675, v = 0.77, l = 8/3},
  pfun = ParametricNDSolveValue[{
     x'[t] == Pr v (y[t] - x[t]),
     y'[t] == R (b/v) x[t] - a y[t] - (b/v) (R - (a v)/b) x[t] z[t],
     z'[t] == a l (x[t] y[t] - z[t]),
     x[0] == y[0] == 0.8, z[0] == 0.92195},
    {x[t], y[t], z[t]}, {t, 0, T}, {R, T}, MaxSteps -> \[Infinity]]];

Manipulate[
 ParametricPlot3D[pfun[R, T] /. t -> u, {u, 0, T}, 
  PlotRange -> 3.7 {{-1, 1}, {-1, 1}, {-1, 1}}, 
  ColorFunction -> Function[{x, y, z, u}, Hue[u]]], {R, 0, 100}, {T, 1, 30}]