Diffusion-driven instability of the periodic solutions for a diffusive system modeling mammalian hair growth

In this paper, we are mainly interested in studying diffusion-driven instability of the bifurcating periodic solution for a diffusive system modeling mammalian hair growth. We say that a periodic solution undergoes diffusion-driven instability, if it is stable with respect to an ODE system, but unst...

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Bibliographic Details
Published in:Nonlinear dynamics 2023-03, Vol.111 (6), p.5799-5815
Main Authors: Yang, Yu, Ju, Xiaowei
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Diffusion rate
Dynamical Systems
Engineering
Growth models
Mammals
Mathematical models
Mechanical Engineering
Original Paper
Stability
Stability analysis
Vibration
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Summary:In this paper, we are mainly interested in studying diffusion-driven instability of the bifurcating periodic solution for a diffusive system modeling mammalian hair growth. We say that a periodic solution undergoes diffusion-driven instability, if it is stable with respect to an ODE system, but unstable in the corresponding diffusive system if suitable diffusion rates are to be chosen. Once the diffusion-driven instability of the periodic solution occurs, new and rich spatiotemporal patterns could be generated. For this particular model, we are able to derive precise conditions on the diffusion rates so that under these conditions the periodic solution could experience diffusion-driven instability. Moreover, we also present some numerical simulations to demonstrate our analytical results.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-08114-x