منابع مشابه
The fractional Keller-Segel model
The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d ≥ 2, but all the solutions are regular in one dimension; a mathematical fact that crucially affects the patterns that can form in the biological system. One of the strongest assumptions...
متن کاملThe Keller-Segel model with small diffusivity
We study the classical model for chemotaxis, the so-called Keller-Segel model, which is a drift-diffusion equation for the cell density coupled with an elliptic equation describing the evolution of the chemoattractant. We investigate the case of small cell diffusivity and, in particular, the hyperbolic limit of the system as the diffusion coefficient goes to zero. Considering a model where the ...
متن کاملPattern Formation (i): the Keller-segel Model
Abstract. We investigate nonlinear dynamics near an unstable constant equilibrium in the classical Keller-Segel model. Given any general perturbation of magnitude δ, we prove that its nonlinear evolution is dominated by the corresponding linear dynamics along a fixed finite number of fastest growing modes, over a time period of ln 1 δ . Our result can be interpreted as a rigourous mathematical ...
متن کاملA stochastic Keller-Segel model of chemotaxis
We introduce stochastic models of chemotaxis generalizing the deterministic KellerSegel 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 cell...
متن کاملThe Stability and Dynamics of a Spike in the One-Dimensional Keller-Segel model
In the limit of a large mass M À 1, and on a finite interval of length 2L, an equilibrium spike solution to the classical Keller-Segel chemotaxis model with a linear chemotactic function is constructed asymptotically. By calculating an asymptotic formula for the translational eigenvalue for M À 1, it is shown that the equilibrium spike solution is unstable to translations of the spike profile. ...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2004
ISSN: 0895-7177
DOI: 10.1016/s0895-7177(04)90528-6