  We study the effect of changes in the parameters of a two-dimensional
potential energy surface on the phase space structures relevant for chemical
reaction dynamics. The changes in the potential energy are representative of
chemical reactions such as isomerization between two structural conformations
or dissociation of a molecule with an intermediate. We present a two degrees of
freedom quartic Hamiltonian that shows pitchfork bifurcation when the
parameters are varied and we derive the bifurcation criteria relating the
parameters. Next, we describe the phase space structures - unstable periodic
orbits and their associated invariant manifolds, and phase space dividing
surfaces - for the systems that can show trajectories undergo reaction defined
as crossing of a potential energy barrier. Finally, we quantify the reaction
dynamics for these systems by obtaining the directional flux and gap time
distribution to illustrate the dependence on total energy and the coupling
strength between the two degrees of freedom.
