Spatio-temporal chaos in a chemotaxis model
Spatio-temporal chaos in a chemotaxis model
复制标题
DOI：
10.1016/j.physd.2010.09.011
复制
发表时间：
2011-02-15
影响因子：
4
通讯作者：
Hillen, Thomas
中科院分区：
文献类型：
--
作者：
Painter, Kevin J.;Hillen, Thomas
在本文中，我们探讨了一个一维的Keller-Segel型模型的趋化性纳入逻辑细胞生长项的动力学。我们证明了该模型的能力，自组织成多个细胞聚集，根据在参数空间中的位置，要么形成一个固定的模式，或经历一个持续的时空序列的合并（两个聚合合并）和新兴的（一个新的聚合出现）。这种时空模式可以进一步细分为时间周期性或时间不规则的方式。后者的数值探索表明一个积极的李雅普诺夫指数（敏感的依赖初始条件），以及丰富的分岔结构。特别是，我们发现固定的模式，分叉到一个路径的周期性模式，在发病前的时空不规则性，经历了一个“双倍”序列。基于这些结果和与其他系统的比较，我们认为，时空不规则性描述了一种形式的时空混沌。我们简要地讨论了我们的结果的背景下，以前的应用程序的趋化性模型，包括肿瘤侵袭，胚胎发育和生态。(C)2010 Elsevier B. V.保留所有权利。
In this paper we explore the dynamics of a one-dimensional Keller-Segel type model for chemotaxis incorporating a logistic cell growth term. We demonstrate the capacity of the model to self-organise into multiple cellular aggregations which, according to position in parameter space, either form a stationary pattern or undergo a sustained spatio-temporal sequence of merging (two aggregations coalesce) and emerging (a new aggregation appears). This spatio-temporal patterning can be further subdivided into either a time-periodic or time-irregular fashion. Numerical explorations into the latter indicate a positive Lyapunov exponent (sensitive dependence to initial conditions) together with a rich bifurcation structure. In particular, we find stationary patterns that bifurcate onto a path of periodic patterns which, prior to the onset of spatio-temporal irregularity, undergo a "periodic-doubling" sequence. Based on these results and comparisons with other systems, we argue that the spatio-temporal irregularity observed here describes a form of spatio-temporal chaos. We discuss briefly our results in the context of previous applications of chemotaxis models, including tumour invasion, embryonic development and ecology. (C) 2010 Elsevier B.V. All rights reserved.