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The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses. (English) Zbl 1061.92059

Summary: We propose an exploited single-species discrete model with stage structure for the dynamics in a fish population for which births occur in a single pulse once per time period. Using the stroboscopic map, we obtain an exact cycle of the system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate as the bifurcation parameter, and are observed to display complex dynamic behaviors, including chaotic bands with period windows, pitch-fork and tangent bifurcation. This suggests that birth pulse provides a natural period or cyclicity that makes the dynamical behavior more complex. Moreover, we show that the timing of harvesting has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. An interesting result is obtained that, after the birth pulse, the earlier culling the mature fish, the larger harvest can tolerate.

MSC:

92D40 Ecology
37N25 Dynamical systems in biology
39A10 Additive difference equations
92D25 Population dynamics (general)
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
39A12 Discrete version of topics in analysis
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