Strange nonchaotic attractors in a fifth-order amplitude equation of Rayleigh–Bénard system near the codimension-two point

We consider a fifth-order amplitude equation for a codimension-two bifurcation point in the presence of a periodically modulated Rayleigh number. It is found, by analysis of Poincaré surfaces and a construction of the bifurcation diagram, that the system exhibits strange nonchaotic behaviour close to the codimension-two point. The Lyapunov exponents associated with these trajectories are calculated using a new method that exploits the underlying symplectic structure of Hamiltonian dynamics.