Discrete Hopf bifurcation for Runge–Kutta methods

An investigation into how well real bifurcations in the family of dynamical systems are approximated as the step-size varies is carried out. The preservation of bifurcation structures and stability under numerical simulations is discussed. In addition, the behaviour of numerical solutions generated by a Runge–Kutta method applied to a dynamical system whose analytical solution undergoes a Hopf bifurcation is investigated. Hopf bifurcation results for the numerical solution are presented and analysed.