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Traveling wavefronts of a prey-predator diffusion system with stage-structure and harvesting. (English) Zbl 1207.92047

Summary: From a biological point of view, we consider a prey-predator-type free diffusion fishery model with stage-structure and harvesting. First, we study the stability of the non-negative constant equilibria. In particular, the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulations. Then, employing the upper and lower solution method, we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system. Numerical simulation is also carried out to illustrate the main result.

MSC:

92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)

Keywords:

stability
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