Cosmological global dynamical systems analysis

We consider a dynamical systems formulation for models with an exponential scalar field and matter linear equation of state in spatially flat isotropic spacetime. In contrast to earlier work, which only considered hyperbolic fixed point analysis, we do center manifold analysis the non-hyperbolic points associated bifurcations. More importantly though, construct monotonic functions Dulac function. Together complete local this leads proofs that describe entire global dynamics these models, thereby complementing previous results literature.