# Plotting basic bifurcation diagram using DiffEq and BifurcationKit.jl

I am trying to plot a very basic bifurcation plot of my simple first order ODE.

``````using DifferentialEquations
using Gnuplot
using BifurcationKit

# this definition makes the dI a vector so have to send in vector initial conditions
# model = @ode_def begin
#     dI = β*I*(1 - 1/𝕽 - I)
# end β 𝕽
odemodel(I, p, t) = p.β*I*(1 - 1/p.𝕽 - I)
prob = ODEProblem(odemodel, 1.0, (0.0, 500.0), (β = 0.04, 𝕽 = 1.2), jac=true)
sol = solve(prob)
``````

I was told the example here would help me out but I am not sure how to get the jacobian of my system.

The jacobian is given in the link you gave `J = (u,p) -> odefun.jac(u,p,0)`

But I don’t have `odefun`… is that something I can create out of the `ODEProblem` object? For example, `𝕽 = 1.0` is a bifurcation point for a transcritical bifurcation and I was wondering if I could show that using `BifurcationKit.jl`

look at `prob.f.jac`

is a bifurcation point for a transcritical bifurcation and I was wondering if I could show that using `BifurcationKit.jl`

Please, see here for a basic example in BifurcationKit.

To compute the bifurcation diagram (BD), you can

1. use automatic BD (see here)
2. use deflated continuation (see here)
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