Population models with non-linear diffusion

Population reaction-diffusion models with nonlinear diffusion are considered. Two classes of the models are investigated – the models of one population and the models of competing populations. In the first class several types of kinetics are considered. The dynamics of the population outbreak is studied for different kinetics. Outbreak spreading front has finite supporter in every time for each case. This phenomenon principally differs from Kolmogorov's waves. In the second class of the models the possibility of appearing stationary spatially nonhomogeneuos solutions is analyzed. Amplification of the Gause principle for spatially distributed competing systems is formulated.