## Title data

Geigant, Edith ; Stoll, Michael:

**Bifurcation analysis of an orientational aggregation model.**

*In:* Journal of Mathematical Biology.
Vol. 46
(2003)
Issue 6
.
- pp. 537-563.

ISSN 0303-6812

DOI: https://doi.org/10.1007/s00285-002-0187-1

## Project information

Project financing: |
E.G. is supported by the Sonderforschungsbereich 256 ‘Nonlinear partial differential equations’ (University of Bonn, Germany). |
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## Abstract in another language

We consider an integro-differential equation for the evolution of a function f on the circle, describing an orientational aggregation process. In the first part we analyze generic bifurcations of steady-state solutions when a single eigenvalue changes sign. Lyapunov-Schmidt reduction leads to the bifurcation equation which is solved explicitly by formal power series. We prove that these series have positive radius of convergence. Two examples

exhibit forward and backward bifurcations, respectively. In the second part we assume that the first and second eigenvalues become positive. Again we use Lyapunov-Schmidt reduction to arrive at the reduced bifurcation system from which we get the bifurcating branches as power series. We calculate the two most important parameters of the reduced system for two examples; one of them has interesting mode interactions which lead to various kinds of time-periodic solutions.

## Further data

Item Type: | Article in a journal |
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Refereed: | Yes |

Keywords: | Actin; Cytoskeleton; Orientational Aggregation; Bifurcation Analysis; Mode Interaction; Power Series Expansion |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | No |

DDC Subjects: | 500 Science > 510 Mathematics 500 Science > 570 Life sciences, biology |

Date Deposited: | 03 Feb 2015 07:26 |

Last Modified: | 08 Jul 2022 08:57 |

URI: | https://eref.uni-bayreuth.de/id/eprint/6225 |