Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects
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This paper is concerned with a delayed predator-prey diffusion model with Neumann boundary conditions. We study the asymptotic stability of the positive constant steady state and the conditions for the existence of Hopf bifurcation. In particular, we show that large diffusivity has no effect on the Hopf bifurcation, while small diffusivity can lead to the fact that spatially nonhomogeneous periodic solutions bifurcate from the positive constant steady-state solution when the system parameters are all spatially homogeneous. Meanwhile, we study the properties of the spatially nonhomogeneous periodic solutions applying normal form theory of partial functional differential equations (PFDEs).
2015 ◽
Vol 25
(11)
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pp. 1550155
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2018 ◽
Vol 5
(1)
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pp. 138-151
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2014 ◽
Vol 24
(04)
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pp. 1450043
2019 ◽
Vol 29
(04)
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pp. 1950043
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2020 ◽
Vol 30
(03)
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pp. 2050037
2020 ◽
Vol 30
(02)
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pp. 2050022
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