Delay-driven spatial patterns in a predator-prey model with constant prey harvesting. (English) Zbl 1490.35029
Summary: 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.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35B36 | Pattern formations in context of PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 35R10 | Partial functional-differential equations |
| 92D30 | Epidemiology |
Software:
PRED_PREYReferences:
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