Open AccessConvective instability in a diffusive predator–prey system
Author(s) -
Hui Chen,
Xuelian Xu
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.74
Subject(s) - steady state (chemistry) , instability , ode , homogeneous , advection , neumann boundary condition , mathematics , diffusion , bifurcation , convection , pattern formation , kinetic energy , reaction–diffusion system , boundary (topology) , statistical physics , mathematical analysis , mechanics , classical mechanics , thermodynamics , physics , chemistry , nonlinear system , genetics , quantum mechanics , biology
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.