  This paper investigates the global structures of periodic orbits that appear
in Rayleigh-B\'enard convection, which is modeled by a two-dimensional
perturbed Hamiltonian model, by focusing upon resonance, symmetry and
bifurcation of the periodic orbits. First, we show the global structures of
periodic orbits in the extended phase space by numerically detecting the
associated periodic points on the Poincar\'e section. Then, we illustrate how
resonant periodic orbits appear and specifically clarify that there exist some
symmetric properties of such resonant periodic orbits which are projected on
the phase space; namely, the period $m$ and the winding number $n$ become odd
when an $m$-periodic orbit is symmetric with respect to the horizontal and
vertical center lines of a cell. Furthermore, the global structures of
bifurcations of periodic orbits are depicted when the amplitude $\varepsilon$
of the perturbation is varied, since in experiments the amplitude of the
oscillation of the convection gradually increases when the Rayleigh number is
raised.
