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Delay-driven spatial patterns in a predator–prey model with constant prey harvesting

Abstract

This paper deals with a predator–prey model with time delay and constant prey harvesting. We investigate the effect of the time delay on the stability of the coexistence equilibrium and demonstrate that time delay can induce spatial patterns. Furthermore, a Hopf bifurcation occurs when the delay increases to a critical value. By applying normal form theory and the center manifold theorem, we develop the explicit formulae that determines the stability and direction of the bifurcating periodic solutions. Finally, we show how the initial condition affects the types of spatial patterns by numerical simulations.

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Correspondence to Michael Pedersen.

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The work is partially supported by the NNSF of China (11771381 and 11801229).

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Gan, W., Lin, Z. & Pedersen, M. Delay-driven spatial patterns in a predator–prey model with constant prey harvesting. Z. Angew. Math. Phys. 73, 120 (2022). https://doi.org/10.1007/s00033-022-01761-5

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  • DOI: https://doi.org/10.1007/s00033-022-01761-5

Keywords

  • Prey harvesting
  • Time delay
  • Hopf bifurcation
  • Spiral wave
  • Target wave

Mathematics Subject Classification

  • 35B32
  • 35B36
  • 92D30