Biological SystemsNo Access

THE OPTIMAL PULSE HARVESTING POLICY ON A SINGLE-SPECIES POPULATION MODEL WITH BIRTH PULSES IN A POLLUTED ENVIRONMENT

BING LIU

Department of Mathematics, Anshan Normal University, Anshan 114007, Liaoning, China

College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China

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and

FENGMEI TAO

Department of Mathematics, Anshan Normal University, Anshan 114007, Liaoning, China

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https://doi.org/10.1142/S0219525907000775Cited by:2 (Source: Crossref)

Abstract

We investigate the dynamics of a single-species model with birth pulses and pulse harvesting in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact 1-period solution of the system whose birth function is a Ricker or Beverton–Holt function and obtain the threshold conditions for their stability. Further, we show the effects of the time of pulse harvesting on the maximum annual-sustainable yield. Our results show that the best time for harvesting is immediately after the birth pulses. Numerical simulation results also show that birth pulses and pulse harvesting make the single-species model in a polluted environment we consider more complex, and the system is dominated by periodic and chaotic solutions.

Keywords:

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