# Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model

@article{Banerjee2012SpatiotemporalEI, title={Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model}, author={S. S. Banerjee and Amar P. Misra and Lamberto Rondoni}, journal={Physica A-statistical Mechanics and Its Applications}, year={2012}, volume={391}, pages={107-112} }

## 20 Citations

SPATIO-TEMPORAL PATTERNING IN A CHEMOTAXIS MODEL

- Mathematics
- 2013

In a recent study (K.J. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxis model, Physica D, 240 (4), 363-375, 2011) a model for chemotaxis incorporating logistic growth was investigated…

Merging-emerging systems can describe spatio-temporal patterning in a chemotaxis model

- Mathematics
- 2013

In a recent study (K.J. Painter and T. Hillen, Spatio-temporal chaos in a chemotaxis
model, Physica D, 240 (4), 363-375, 2011) a model for chemotaxis incorporating
logistic growth was investigated…

Spatial pattern formation in the Keller-Segel model with a logistic source

- MathematicsComput. Math. Appl.
- 2013

Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth

- Mathematics
- 2014

This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a -dimensional box . It is proved that given any general perturbation of magnitude…

A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term

- Mathematics
- 2013

This paper deals with a Neumann boundary value problem for a Keller-Segel model with a cubic source term in a d-dimensional box , which describes the movement of cells in response to the presence of…

Numerical approximation of one model of bacterial self-organization

- Mathematics
- 2012

This paper presents finite difference approximations of one dimensional in space mathematical model of a bacterial self-organization. The dynamics of such nonlinear systems can lead to formation of…

Spatiotemporal chaos in mixed linear–nonlinear two-dimensional coupled logistic map lattice

- Physics
- 2018

Turing instability for a attraction-repolsion chemotaxis system with logistic growth

- Mathematics
- 2020

In this paper, we investigate the nonlinear dynamics for an attraction-repulsion chemotaxis Keller-Segel model with logistic source term u1t = d1∆u1 − χ∇(u1∇u2) + ξ∇(u1∇u3) + g(u), x ∈ Td, t > 0, u2t…

Mathematical models for chemotaxis and their applications in self-organisation phenomena.

- BiologyJournal of theoretical biology
- 2018

## References

SHOWING 1-10 OF 43 REFERENCES

A user’s guide to PDE models for chemotaxis

- Computer ScienceJournal of mathematical biology
- 2009

This paper explores in detail a number of variations of the original Keller–Segel model of chemotaxis from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form.

Classical solutions and pattern formation for a volume filling chemotaxis model.

- BiologyChaos
- 2007

It is concluded that the emerging process of pattern formation is due to cell growth, and classical solutions to a generalized chemotaxis model, which includes the volume filling effect expressed through a nonlinear squeezing probability is established.

On Chemotaxis Models with Cell Population Interactions

- Mathematics
- 2010

This paper extends the volume filling chemotaxis model by taking into account the cell population interactions, which is a modification of the Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear).

Physical mechanisms for chemotactic pattern formation by bacteria.

- Computer ScienceBiophysical journal
- 1998

Collapsing bacterial cylinders.

- EngineeringPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is shown that cylindrical collapse involves a delicate balance in which bacterial attraction and diffusion nearly cancel, leading to corrections to the collapse laws expected from dimensional analysis.

Initiation of slime mold aggregation viewed as an instability.

- EconomicsJournal of theoretical biology
- 1970

Chemoreceptors in bacteria.

- BiologyScience
- 1969

For a hundred years it was known that motile bacteria are attracted to a variety of small organic molecules. However, few scientists were interested in bacterial chemotaxis, probably because they…