Warning in the simulation part of the Barrier certificates example from the tutorials.

[hurak]

The simulation part of the Barrier certificates for collision avoidance example, that is, the code

import DifferentialEquations, Plots, ImplicitPlots
function phase_plot(f, B, g₁, h₁, quiver_scaling, Δt, X0, solver = DifferentialEquations.Tsit5())
    X₀plot = ImplicitPlots.implicit_plot(h₁; xlims=(-2, 3), ylims=(-2.5, 2.5), resolution = 1000, label="X₀", linecolor=:blue)
    Xᵤplot = ImplicitPlots.implicit_plot!(g₁; xlims=(-2, 3), ylims=(-2.5, 2.5), resolution = 1000, label="Xᵤ", linecolor=:teal)
    Bplot  = ImplicitPlots.implicit_plot!(B; xlims=(-2, 3), ylims=(-2.5, 2.5), resolution = 1000, label="B = 0", linecolor=:red)
    Plots.plot(X₀plot)
    Plots.plot!(Xᵤplot)
    Plots.plot!(Bplot)
    ∇(vx, vy) = [fi(x[1] => vx, x[2] => vy) for fi in f]
    ∇pt(v, p, t) = ∇(v[1], v[2])
    function traj(v0)
        tspan = (0.0, Δt)
        prob = DifferentialEquations.ODEProblem(∇pt, v0, tspan)
        return DifferentialEquations.solve(prob, solver, reltol=1e-8, abstol=1e-8)
    end
    ticks = -5:0.5:5
    X = repeat(ticks, 1, length(ticks))
    Y = X'
    Plots.quiver!(X, Y, quiver = (x, y) -> ∇(x, y) / quiver_scaling, linewidth=0.5)
    for x0 in X0
        Plots.plot!(traj(x0), vars=(1, 2), label = nothing)
    end
    Plots.plot!(xlims = (-2, 3), ylims = (-2.5, 2.5))
end

phase_plot(f, value(B), g₁, h₁, 10, 30.0, [[x1, x2] for x1 in 1.2:0.2:1.7, x2 in -0.35:0.1:0.35])

gives the warning

Warning: At t=4.423118290940107, dt was forced below floating point epsilon 8.881784197001252e-16, and step error estimate = 1.139033855908175. Aborting. There is either an error in your model specification or the true solution is unstable (or the true solution can not be represented in the precision of Float64).
└ @ SciMLBase ~/.julia/packages/SciMLBase/BaHpR/src/integrator_interface.jl:623