Pattern Formation in Keller–Segel Chemotaxis Models with Logistic Growth
نویسندگان
چکیده
منابع مشابه
Pattern Formation in Keller-Segel Chemotaxis Models with Logistic Growth
In this paper, we investigate the pattern formation in Keller–Segel chemotaxis over multi– dimensional bounded domains subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as chemoattraction rate χ increases. Then, using Crandall–Rabinowitz local theory with χ being the bifurcation parameter, we obtain the existence of no...
متن کاملPattern formation and nonlocal logistic growth.
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and long-range interactions. Domain walls between regions of different order parameter are expressed as soliton solutions of the reduced dynamics for nearest-neighb...
متن کاملAnalysis of logistic growth models.
A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitati...
متن کاملBasic Mechanisms Driving Complex Spike Dynamics in a Chemotaxis Model with Logistic Growth
Recently, Wang and Hillen [Chaos 17 (3) (2007) 037108–037108] introduced a modified Keller-Segel model with logistic growth that exhibits complex spatiotemporal dynamics of spikes. These dynamics are driven by merging of spikes on one hand, and spike insertion on the other. In this paper we analyse the basic mechanisms that initiate and sustain these events. We identify two distinguished regime...
متن کاملStochastic nonlinear dynamics pattern formation and growth models
Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature.
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: International Journal of Bifurcation and Chaos
سال: 2016
ISSN: 0218-1274,1793-6551
DOI: 10.1142/s0218127416500334