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**Dynamical analysis of a delayed reaction-diffusion predator-prey system.**
*(English)*
Zbl 1256.35183

Summary: This work deals with the analysis of a delayed diffusive predator-prey system under Neumann boundary conditions. The dynamics are investigated in terms of the stability of the nonnegative equilibria and the existence of Hopf bifurcation by analyzing the characteristic equations. The direction of Hopf bifurcation and the stability of bifurcating periodic solution are also discussed by employing the normal form theory and the center manifold reduction. Furthermore, we prove that the positive equilibrium is asymptotically stable when the delay is less than a certain critical value and unstable when the delay is greater than the critical value.

### MSC:

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

92D25 | Population dynamics (general) |

35B35 | Stability in context of PDEs |

35B32 | Bifurcations in context of PDEs |

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\textit{Y. Zhu} et al., Abstr. Appl. Anal. 2012, Article ID 323186, 23 p. (2012; Zbl 1256.35183)

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### References:

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