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Séminaire du LJLL - 03 02 2017 14h00 : S. Yasuda
Shugo Yasuda (Université de Hyogo)
Linear instability and pattern formation in a kinetic chemotaxis equation
Abstract
Pattern formations are ubiquitous in biological phenomena. This talk is concerned with the linear instability and pattern formation of the population density of chemotactic bacteria described by a kinetic chemotaxis equation coupled with a reaction-diffusion equation for the chemical attractant. We obtain a linear instability condition for which the uniform stationary state of the population density of bacteria becomes linearly unstable and where periodic patterns are generated. We also numerically demonstrate this pattern formation by Monte Carlo simulations in which we vary the parameters involved in the linear instability condition. Some tentative results of Monte Carlo simulations for the traveling waves will also be presented in the talk.