  We investigate the dynamics of closed FRW universe and anisotropic Bianchi
type-IX universe characterized by two scale factors in a gravity theory
including a higher curvature (Gauss-Bonnet) term. The presence of the
cosmological constant creates a critical point of saddle type in the phase
space of the system. An orbit starting from a neighborhood of the separatrix
will evolve toward the critical point, and it eventually either expands to the
de Sitter space or collapses to the big crunch. In the closed FRW model, the
dynamics is reduced to hyperbolic motions in the two-dimensional center
manifold, and the system is not chaotic. In the anisotropic model, anisotropy
introduces the rotational mode, which interacts with the hyperbolic mode to
present a cylindrical structure of unstable periodic orbits in the neighborhood
of the critical point. Due to the non-integrability of the system, the
interaction of rotational and hyperbolic modes makes the system chaotic, making
it impossible for us to predict the final fate of the universe. We find that
the chaotic dynamics arises from the fact that orbits with even small
perturbations around the separatrix oscillate in the neighborhood of the
critical point before finally expanding or collapsing. The chaotic character is
also evidenced by the fractal structures in the basins of attraction.
