Leírás
University of Szeged, Bolyai Institute, Differential Equations Seminar
Abstract. In this talk, we are interested in pattern dynamics for a modified Leslie-Gower-type model with cross-diffusion and indirect predation effect. Firstly, we prove the well-posedness of the considered model. Then linear stability analysis shows that the cross-diffusion is the key mechanism of spatiotemporal pattern formation. Amplitude equations are derived near Turing bifurcation point to interpret pattern selection among spot pattern, stripe pattern and the mixture of spots and stripes pattern, which reflects the species' spatially inhomogeneous distribution. Finally, numerical simulations illustrate the effectiveness of all theoretical results, and it is also found that the fear has great influence on spatially inhomogeneous distribution of the two species under certain cross-diffusivity.