Рolynomial models of populations with autotaxis: “travelling wave” solutions

The conceptual model of a population with attractant being a system of a “reaction-diffusion-crossdiffusion” type is considered. The analysis of “travelling wave” solutions of a model with polynomial functions of population growth (Malthus, logistics, Alle type) and polynomial intensity of autotaxis is carried out in a neighbourhood of local equilibria by methods of bifurcation theory. The different spatially non-homogeneous wave regimes (wave-fronts, impulses, trains etc.) are described, an evolution of travelling wave characteristics with increase of degrees of growth and taxis polynomial functions, variation of model parameters and velocity of spread was analysed sequentially. The possibilities of application of obtained results under research of a phenomenon of pattern density formation in the spatially distributed populations (such as plancton communities and phytofage populations) are discussed. The founded non-monotone wave regimes could be interpreted as moving spatially non-homogeneous distributions (patches) of population density.