Pattern formation (I): The Keller–Segel model
نویسندگان
چکیده
منابع مشابه
Pattern 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 کاملPattern Formation of the FitzHugh-Nagumo Model: Cellular Automata Approach
FitzHugh-Nagumo (FHN) model is a famous Reaction-Diffusion System which first introduced for the conduction of electrical impulses along a nerve fiber. This model is also considered as an abstract model for pattern formation. Here, we have used the Cellular Automata method to simulate the pattern formation of the FHN model. It is shown that the pattern of this model is very similar to those...
متن کاملpattern formation of the fitzhugh-nagumo model: cellular automata approach
fitzhugh-nagumo (fhn) model is a famous reaction-diffusion system which first introduced for the conduction of electrical impulses along a nerve fiber. this model is also considered as an abstract model for pattern formation. here, we have used the cellular automata method to simulate the pattern formation of the fhn model. it is shown that the pattern of this model is very similar to those of ...
متن کاملPattern formation in a generalized chemotactic model.
Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of...
متن کاملTissue Interaction Model for Skin Pattern Formation
A nonlinear analysis of a mechanical model for biological pattern formation, SIAM J. pattern selection in a mechanical model for morphogenesis, Mathematical modelling of the generation and onset of spatial patterns in the early stages of embryonic development — reaction-diffusion equations, chemotaxis equations, mechanochemical force balance equations. (1988): the communication between differen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2010
ISSN: 0022-0396
DOI: 10.1016/j.jde.2010.07.025