Quantifying "damping" rate of ODE

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This turned out to be a great solution, thank you!

For those interested, I ended up doing this to get the eigenvalue with largest real part.:

     using ForwardDiff, NonlinearSolve
     function stability(inits, parameters) #initial conditions and parameters
        NLprob = NonlinearProblem(Alpha_Temp_B, inits, parameters)  # find roots of model Alpha_Temp_B(u,p)
        NLsol = solve(NLprob, NewtonRaphson())  # find the steady-state
        J = ForwardDiff.jacobian(u -> Alpha_Temp_B(u, parameters), NLsol.u)  # get Jacobian
        max_real = maximum(real.(eigen(J).values)) #get eigenvalue with maximum real part
     end

I had previously found convenient code to do this here: Incorrect bifurcation diagram bifurcationkit.jl - #4 by dawbarton

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