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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:
35K51Second-order parabolic systems, initial bondary value problems
35Q92PDEs in connection with biology and other natural sciences
37N25Dynamical systems in biology
92D25Population dynamics (general)
35B10Periodic solutions of PDE
35B32Bifurcation (PDE)
35B35Stability of solutions of PDE
35K91Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
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