A stochastic Keller–Segel model of chemotaxis |
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Authors: | Pierre-Henri Chavanis |
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Affiliation: | aLaboratoire de Physique Théorique (CNRS UMR 5152), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France |
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Abstract: | We introduce stochastic models of chemotaxis generalizing the deterministic Keller–Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean’s approach, we derive the exact kinetic equation satisfied by the density distribution of cells. In the mean field limit where statistical correlations between cells are neglected, we recover the Keller–Segel model governing the smooth density field. We also consider hydrodynamic and kinetic models of chemotaxis that take into account the inertia of the particles and lead to a delay in the adjustment of the velocity of cells with the chemotactic gradient. We make the connection with the Cattaneo model of chemotaxis and the telegraph equation. |
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Keywords: | Chemotaxis Self-organization Nonlinear dynamics Fluctuations Stochastic processes Long-range interactions |
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