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Literature DB >> 1933036

Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.

P K Maini¹, M R Myerscough, K H Winters, J D Murray.

Abstract

We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989, J. exp. Zool. 251, 186-202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.

Mesh：

Year: 1991 PMID： 1933036 DOI： 10.1007/bf02461550

Source DB: PubMed Journal: Bull Math Biol ISSN： 0092-8240 Impact factor: 1.758

15 in total

1. Pattern regulation in epimorphic fields.

Authors: V French; P J Bryant; S V Bryant
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Authors: George F Oster; Neil Shubin; James D Murray; Pere Alberch
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5. Initiation of slime mold aggregation viewed as an instability.

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7. On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings.

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9. The relationship between cell division and melanocyte differentiation in epidermal cultures from mouse embryos.

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2. Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem.

Authors: Xuefeng Wang; Qian Xu
Journal: J Math Biol Date: 2012-04-18 Impact factor: 2.259

Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.

1. Pattern regulation in epimorphic fields.

2. EVOLUTION AND MORPHOGENETIC RULES: THE SHAPE OF THE VERTEBRATE LIMB IN ONTOGENY AND PHYLOGENY.

Review 3. Pattern formation models and developmental constraints.

4. Positional information and the spatial pattern of cellular differentiation.

5. Initiation of slime mold aggregation viewed as an instability.

6. Positional information and pattern formation.

7. On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings.

8. A model for generating aspects of zebra and other mammalian coat patterns.

9. The relationship between cell division and melanocyte differentiation in epidermal cultures from mouse embryos.

10. Size-dependent pigmentation-pattern formation in embryos of Alligator mississippiensis: time of initiation of pattern generation mechanism.

1. A gene network model accounting for development and evolution of mammalian teeth.

2. Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem.

3. Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems.

4. Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism.

Review 5. A user's guide to PDE models for chemotaxis.

6. Wing vein patterns of the Hemiptera insect Orosanga japonicus differ among individuals.

Review 7. Mathematically guided approaches to distinguish models of periodic patterning.

8. Chemotaxis and chemokinesis in eukaryotic cells: the Keller-Segel equations as an approximation to a detailed model.

9. Orientation of Turing-like Patterns by Morphogen Gradients and Tissue Anisotropies.

10. A mathematical analysis of a model for tumour angiogenesis.