Traveling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities
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In this paper, the authors studied the branching instability in the hyperbolic Keller-Segel system with logistic sensitivity, where repulsive and attractive forces, acting on a conservative system, create stable traveling patterns or branching instabilities.Abstract:
How can repulsive and attractive forces, acting on a conservative system, create stable traveling patterns or branching instabilities? We have proposed to study this question in the framework of the hyperbolic Keller-Segel system with logistic sensitivity. This is a model system motivated by experiments on cell communities auto-organization, a field which is also called socio-biology. We continue earlier modeling work, where we have shown numerically that branching patterns arise for this system and we have analyzed this instability by formal asymptotics for small diffusivity of the chemo-repellent. Here we are interested in the more general situation, where the diffusivities of both the chemo-attractant and the chemo-repellent are positive. To do so, we develop an appropriate functional analysis framework. We apply our method to two cases. Firstly we analyze steady states. Secondly we analyze traveling waves when neglecting the degradation coefficient of the chemo-repellent; the unique wave speed appears through a singularity cancelation which is the main theoretical difficulty. This shows that in different situations the cell density takes the shape of a plateau. The existence of steady states and traveling plateaus are a symptom of how rich the system is and why branching instabilities can occur. Numerical tests show that large plateaus may split into smaller ones, which remain stable.read more
Citations
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References
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Branched swarming patterns on a synthetic medium formed by wild-type Bacillus subtilis strain 3610: detection of different cellular morphologies and constellations of cells as the complex architecture develops.
Daria Julkowska,Daria Julkowska,Michal Obuchowski,Michal Obuchowski,I. Barry Holland,Simone J. Séror +5 more
TL;DR: A detailed microscopic in situ analysis of swarms 1 and 2 revealed varied cell morphologies and a remarkable series of events, with cells assembling into different 'structures', as the architecture of the swarm developed.
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Existence of solutions of the hyperbolic Keller-Segel model
TL;DR: In this paper, the authors considered the hyperbolic Keller-Segel model with quorum sensing, a model describing the collective cell movement due to chemical signalling with a flux limitation for high cell densities.
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Existence of solutions of the hyperbolic Keller-Segel model
TL;DR: In this paper, the authors considered the hyperbolic Keller-Segel model with quorum sensing, a model describing the collective cell movement due to chemical signalling with a flux limitation for high cell densities.