  We investigate the qualitative evolution of (D+1)-dimensional cosmological
models in f(R) gravity for the general case of the function f(R). The analysis
is specified for various examples, including the (D+1)-dimensional
generalization of the Starobinsky model, models with polynomial and exponential
functions. The cosmological dynamics are compared in the Einstein and Jordan
representations of the corresponding scalar-tensor theory. The features of the
cosmological evolution are discussed for Einstein frame potentials taking
negative values in certain regions of the field space.
