On bifurcations in complex ecological systems with diffusion and noise

We investigate here several methods for the qualitative investigation of complex ecological systems including diffusion and noise. Assuming that the systems are described by diffusion equations or Fokker-Planck equations, we formulate for gradient-type dynamical systems several statements about the number and type of possible bifurcations using theorems of catastrophe theory. We introduce stochastic potentials, present exact and approximate solutions. In the case of general dynamical systems we show that the case of strong noise may be appropriately described by expansions of the stochastic potential with respect to reciprocal noise. Finally we present examples for the bifurcations of the biomass.