Analysis of Hopf/Hopf bifurcations in nonlocal hyperbolic models for self-organised aggregations

P.-L. Buono, R. Eftimie (Lead / Corresponding author)

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    Abstract

    The modelling and investigation of complex spatial and spatio-temporal patterns exhibited by a various self-organised biological aggregations has become one of the most
    rapidly-expanding research areas. Generally, the majority of the studies in this area either try to reproduce numerically the observed patterns, or use existence results to
    prove analytically that the models can exhibit certain types of patterns. Here, we focus on a class of nonlocal hyperbolic models for self-organised movement and aggregations,
    and investigate the bifurcation of some spatial and spatio-temporal patterns observed numerically near a codimension-2 Hopf/Hopf bifurcation point. Using weakly nonlinear
    analysis and the symmetry of the model, we identify analytically all types of solutions that can exist in the neighbourhood of this bifurcation point. We also discuss the stability
    of these solutions, and the implication of these stability results on the observed numerical patterns.
    Original languageEnglish
    Pages (from-to)327-357
    Number of pages31
    JournalMathematical Models and Methods in Applied Sciences
    Volume24
    Issue number2
    Early online date20 Nov 2013
    DOIs
    Publication statusPublished - Feb 2014

    Keywords

    • Nonlocal hyperbolic model
    • self-organised aggregations
    • bifurcation and symmetry

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