RT Journal Article
T1 Bifurcation sequences in a discontinuous piecewise-smooth map combining constant-catch and threshold-based harvesting strategies
A1 Lois-Prados, Cristina
A1 Hilker, Frank
K1 nonsmooth discrete one-dimensional dynamical system
K1 discontinuous difference equation
K1 border-collision bifurcation
K1 fishery model
K1 population harvesting
K1 harvest control rule
AB We consider a harvesting strategy that allows constant catches if the population size is above a certain threshold value (to obtain predictable yield) and no catches if the population size is below the threshold (to protect the population). We refer to this strategy as threshold constant-catch (TCC) harvesting. We provide analytical and numerical results when applying TCC to monotone population growth models. TCC remedies the tendency to fishery collapse of pure constant-catch harvesting and provides a buffer for quotas larger than the maximum sustainable yield. From a dynamical systems point of view, TCC gives rise to a piecewise-smooth map with a discontinuity at the threshold population size. The dynamical behavior includes border-collision bifurcations, basin boundary metamorphoses, and boundary-collision bifurcation. We further find Farey trees, a slightly modified truncated skew tent map scenario, and the bandcount incrementing scenario. Our results underline, on the one hand, the protective function of thresholds in harvest control rules. On the other hand, they highlight the dynamical complexities due to discontinuities that can arise naturally in threshold-based harvesting strategies.
PB Society for Industrial and Applied Mathematics
SN 1536-0040
YR 2022
FD 2022
LK http://hdl.handle.net/10347/31833
UL http://hdl.handle.net/10347/31833
LA eng
NO C. Lois-Prados, F. M. Hilker (2022). Bifurcation sequences in a discontinuous piecewise-smooth map combining constant-catch and threshold-based harvesting strategies. SIAM Journal on Applied Dynamical Systems, 21(1), 470-499.
NO First Published in SIAM Journal of Applied Dynamical Systems in 2022, published by the Society for Industrial and Applied Mathematics (SIAM).
NO The first author's work was partially supported by PhD scholarship FPU18/00719 (Ministerio de Ciencia, Innovación y Universidades, Spain) and research grants MTM2016-75140-P (AEI/FEDER, UE), ED431C2019/02 (Xunta de Galicia). Osnabrück University provided funding to the first author to visit the Institute of Environmental Systems Research for a period of six weeks, during which parts of this work were completed.
DS Minerva
RD 24 abr 2026