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Author Bose, Koushiki ♦ Cox, Tyler ♦ Silvestri, Stefano ♦ Varin, Patrick ♦ Holzer, Sponsors Matt ♦ Scheel, Arnd
Source CiteSeerX
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract The purpose of this paper is to explore spatio-temporal pattern formation via invasion fronts in the one and two dimensional Keller-Segel chemotaxis model. Simulations show that solutions which begin near an unstable homogeneous equilibrium evolve into periodic patterns as time increases. These patterns form a quasi-equilibrium which by a secondary invasion process develops a new pattern with double the wavelength–a process known as coarsening. For cell densities close to the threshold of instability, we obtain expansions for the speed of the primary invasion front and the selected wavelength. In order to study the coarsening dynamics, we explore the linearization about periodic equilibria. The unstable eigenvalues of this linearization and their corresponding eigenfunctions reveal two different coarsening modes, a “parasitic ” mode in which one peak grows at the expense of the other and an “aggregate” mode in which neighboring peaks move towards each other and merge to form a larger peak. In two space dimensions, we show that the initial invasion front creates a periodic pattern with no transverse dependence. Transverse patterning arises as a result of a transverse instability of these periodic patterns in the leading edge of the front as we show by numerically examining the linearization at these periodic patterns. Keywords. chemotaxis, spreading speeds, double roots, linear stability, coarsening
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article