| Abstract: |
| In this talk, we study the case that some species migrate from densely populated
areas into sparsely populated areas to avoid crowding, and investigate a more general
parabolic system by considering density-dependent dispersion as a regulatory mechanism of the cyclic changes. Here the probability that an animal moves from the
point x1 to x2 depends on the density at x1. Under certain conditions, we apply the
higher terms in the Taylor series and the center manifold method to obtain the local
behavior around a non-hyperbolic point of codimension one in the phase plane, and
use the Lie symmetry reduction method to explore bounded traveling wave solutions.
By virtue of the Abel integral equation we
derive the asymptotic expansion of bounded solutions in the Banach space, and use
the asymptotic formula to construct approximate solutions. Numerical simulation
and biological explanation are presented. |
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