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A note on Hopf bifurcations in a delayed diffusive Lotka-Volterra predator-prey system. (English) Zbl 1231.35096

Summary: The diffusive Lotka-Volterra predator-prey system with two delays is reconsidered here. The stability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations, and our results complement earlier ones. We also obtain that in a special case, a Hopf bifurcation of spatial inhomogeneous periodic solutions occurs in the system.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35Q92 PDEs in connection with biology, chemistry and other natural sciences
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
35B10 Periodic solutions to PDEs
35B32 Bifurcations in context of PDEs
35B35 Stability in context of PDEs
35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
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References:

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