| Abstract: |
| In this talk, we present a nonlinear parabolic system incorporating dispersion to model bacterial aggregation dynamics. In contrast to models without dispersion, the inclusion of dispersive effects enables the propagation of bacterial clusters, suggesting that dispersion may serve as a regulatory mechanism in colony behavior. Through theoretical analysis and numerical simulations, we show that an initially random bacterial distribution evolves into a periodic wave pattern, in the absence of dispersion, this pattern ultimately transitions into a stationary solitary wave. |
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