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Interaction between harvesting intervention and birth perturbation in an age-structured model
Haiyan Xu1, Zhigui Lin2, Carlos Alberto Santos3
1School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China.
Abstract:
An age-structured fish model with birth and harvesting pulses is established, where birth pulses are responsible for increasing the amount of fish due to the constant multiple placement of juveniles, and harvesting pulses describe the decrease of fish due to fishing activities. The principal eigenvalue as a threshold value depending on the harvesting and birth intensity is firstly investigated by three different ways. The asymptotic behavior of the population is fully investigated and sufficient conditions for the species to be extinct or persist are given. Numerical simulations suggest that interaction between negative harvesting intervention and positive birth perturbation decides extinction and persistence of the species. It is possible to transform between expansion and extinction of species for sustainable development of fishery resources by choosing appropriate pulse intensities and perturbation timing.
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