×

zbMATH — the first resource for mathematics

Harvesting induced fluctuations: insights from a threshold management policy. (English) Zbl 1106.92069
Summary: It is shown that in a deterministic context, a threshold policy can induce cyclic behavior in an otherwise exploited stable population. These dynamics ensue as a result of the combination of the degree of harvesting pressure and more protective threshold densities. Virtual equilibrium in variable structure systems plays a determinant role in this dynamical outcome.

MSC:
92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
93C95 Application models in control theory
39A11 Stability of difference equations (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chau, N.P., Destabilizing effect of periodic harvest on population dynamics, Ecological modelling, 127, 1, (2000)
[2] Clark, C.W., Bioeconomics modelling and fisheries management, (1985), John Wiley & Sons USA
[3] Costa, M.I.S.; Kaszkurewicz, E.; Bhaya, A.; Hsu, L., Achieving global convergence to an equilibrium population in predator – prey systems by the use of discontinuous harvesting policy, Ecological modelling, 128, 89, (2000)
[4] Fryxell, J.; Smith, I.M.; Lynn, D.H., Evaluation of alternative harvesting strategies using experimental microcosms, Oikos, 111, 143, (2005)
[5] Goh, B.S., Stability in a stock-recruitment model of an exploited fishery, Mathematical biosciences, 33, 359, (1977) · Zbl 0379.92018
[6] Jonzén, N.; Ranta, E.; Lundberg, P.; Kaitala, V.; Lindén, H., Harvesting induced fluctuations?, Wildlife biology, 9, 59, (2003)
[7] Meza, M.E.M.; Bhaya, A.; Kaszkurewicz, E.; da Silveira Costa, M.I., Threshold policies control for predator – prey systems using a control Liapunov function approach, Theoretical population biology, 67, 4, 273, (2005) · Zbl 1072.92054
[8] Quinn, T.J.; Deriso, R.B., Quantitative fish dynamics, Biological resource management series, (2000), Oxford University Oxford
[9] Quinn, T.J.; Fagen, R.; Zheng, J., Threshold management policies for exploited populations, Canadian journal of fisheries and aquatic sciences, 47, 10, 2016, (1990)
[10] Sabo, J.L., Stochasticity, population dynamics and trigger harvest of nonnative predators, Ecology, 86, 2239, (2005)
[11] Silvert, W., Anomalous enhancement of Mean population levels by harvesting, Mathematical biosciences, 42, 253, (1978)
[12] Utkin, V.L., Sliding modes and their applications in variable structure systems, (1978), Mir Moscow
[13] Utkin, V.L., Sliding modes in control and optimization, (1992), Springer Berlin · Zbl 0748.93044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.