The Influence of Dirichlet Boundary Conditions on the Dynamics for a Diffusive Predator–Prey System
2019 ◽
Vol 29
(09)
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pp. 1950113
Keyword(s):
A reaction–diffusion predator–prey system with homogeneous Dirichlet boundary conditions describes the lethal risk of predator and prey species on the boundary. The spatial pattern formations with the homogeneous Dirichlet boundary conditions are characterized by the Turing type linear instability of homogeneous state and bifurcation theory. Compared with homogeneous Neumann boundary conditions, we see that the homogeneous Dirichlet boundary conditions may depress the spatial patterns produced through the diffusion-induced instability. In addition, the existence of semi-trivial steady states and the global stability of the trivial steady state are characterized by the comparison technique.
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pp. 0
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pp. 2071-2109
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