tangent_integrator not compatible with stiff solvers

Hi,
as shown here https://discourse.julialang.org/t/chaostools-tangent-integrator-stiff-solvers/26464, the tangent_integrator errors, if one provides an algorithm, which uses ForwardDiff.jl to calculate the Jacobian, etc. This is the case for all stiff solvers. One can avoid using auto-differentiation by passing autodiff=false to the algorithm, e.g. Rodas5(autodiff=false) but we often want this feature!

The error is due to caching the Jacobi-matrix in the create_tangent function (https://github.com/JuliaDynamics/DynamicalSystemsBase.jl/blob/master/src/dynamicalsystem.jl#L343-L355)

# IIP Tangent Space dynamics
function create_tangent(@nospecialize(f::F), @nospecialize(jacobian::JAC), J::JM,
    ::Val{true}, ::Val{k}) where {F, JAC, JM, k}
    J = deepcopy(J)
    tangentf = (du, u, p, t) -> begin
        uv = @view u[:, 1]
        f(view(du, :, 1), uv, p, t)
        jacobian(J, uv, p, t)
        mul!((@view du[:, 2:(k+1)]), J, (@view u[:, 2:(k+1)]))
        nothing
    end
    return tangentf
end

Especially line 346:
J = deepcopy(J).

A workaround is described here http://docs.juliadiffeq.org/latest/basics/faq.html#I-get-Dual-number-errors-when-I-solve-my-ODE-with-Rosenbrock-or-SDIRK-methods.

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Start in src/dynamicalsystem.jl, especially create_tangent around lines 343-355, and review how the cached Jacobian is used with ForwardDiff.jl-based stiff solver algorithms. Reproduce the tangent_integrator failure with a stiff solver using autodiff, then verify that the integration works without requiring autodiff=false.