Convective instability in a diffusive predator-prey system

Chen Hui and Xu Xuelian: Convective instability in a diffusive predator-prey system. (2021)

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It is well known that biological pattern formation is the Turing mechanism, in which a homogeneous steady state is destabilized by the addition of diffusion, though it is stable in the kinetic ODEs. However, steady states that are unstable in the kinetic ODEs are rarely mentioned. This paper concerns a reaction diffusion advection system under Neumann boundary conditions, where steady states that are unstable in the kinetic ODEs. Our results provide a stabilization strategy for the same steady state, the combination of large advection rate and small diffusion rate can stabilize the homogeneous equilibrium. Moreover, we investigate the existence and stability of nonconstant positive steady states to the system through rigorous bifurcation analysis.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2021
Number: 74
ISSN: 1417-3875
Number of Pages: 9
Language: English
DOI: 10.14232/ejqtde.2021.1.74
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: p. 8-9. ; összefoglalás angol nyelven
Date Deposited: 2021. Nov. 11. 11:20
Last Modified: 2021. Nov. 11. 11:20

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