Travelling front solutions arising in the chemotaxis-growth model | Zendy

Mitsuo Funaki | Zendy; Masayasu Mimura | Zendy; Tohru Tsujikawa | Zendy

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Travelling front solutions arising in the chemotaxis-growth model

Author(s) -

Mitsuo Funaki,

Masayasu Mimura,

Tohru Tsujikawa

Publication year - 2006

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/141

Subject(s) - chemotaxis , bistability , front (military) , diffusion , advection , limit (mathematics) , reaction–diffusion system , traveling wave , pattern formation , physics , dynamics (music) , mathematical analysis , statistical physics , mathematics , mechanics , chemistry , biology , thermodynamics , meteorology , biochemistry , receptor , genetics , quantum mechanics , acoustics

We consider a bistable reaction-diffusion-advection system describing the growth of biological individuals which move by diffusion and chemotaxis. We use the singular limit procedure to study the dynamics of growth patterns arising in this system. It is shown that travelling front solutions are transversally stable when the chemotactic effect is weak and, when it becomes stronger, they are destabilized. Numerical simulations reveal that the destabilized solution evolves into complex patterns with dynamic network-like structures.

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