Rocky Mountain Journal of Mathematics

Topological Description of a Non-Differentiable Bioeconomics Model

Article information

Source
Rocky Mountain J. Math., Volume 35, Number 4 (2005), 1133-1155.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181069680

Digital Object Identifier
doi:10.1216/rmjm/1181069680

Mathematical Reviews number (MathSciNet)
MR2178981

Zentralblatt MATH identifier
1214.91083

Subjects
Primary: 92D25: Population dynamics (general) 34C 58F14 58F21

Citation

González-Olivares, E.; Sáez, E.; Stange, E.; Szántó, I. Topological Description of a Non-Differentiable Bioeconomics Model. Rocky Mountain J. Math. 35 (2005), no. 4, 1133--1155. doi:10.1216/rmjm/1181069680. https://projecteuclid.org/euclid.rmjm/1181069680

References

• E.S. Amundsen, T. Bjorndal and J.M. Conrad, Open access harvesting of the Northeast Atlantic Minke whale, Environ. Res. Econ. 6 (1995), 167-185.
• D.K. Arrowsmith and C.M. Place, Dynamical systems, Chapman and Hall, 1992.
• A. Berryman, A.P. Gutierrez and R. Arditi, Credible, parsimonious and useful predator-prey models\emdash/A reply to Abrams, Gleeson, and Sarnelle, Ecology 76 (1995), 1980-1985.
• T. Bjorndal and J.M. Conrad, The dynamic of an open access fishery, Canad. J. Economy 20 (1987), 74-85.
• T.R. Blows and N.G. Lloyd, The number of limit cycles of certain polynomial differential equations, Proc. Royal Soc. Edinburgh 98 (1984), 215-239.
• C.W. Clark, Mathematical bioeconomics: The optimal management of renewable resources, 2nd ed., John Wiley and Sons, New York, 1990.
• F. Dumortier, Singularities of vector fields, Monograf. Mat. N$^\texto$ 32, Inst. Mat. Pura Apl., Rio de Janeiro, 1978.
• H.I. Freedman, Stability analysis of a predator-prey system with mutual interference and density dependent death rates, Bull. Math. Biol. 41 (1979), 677-692.
• J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer-Verlag, New York, 1983.
• R. Hannesson, Bioeconomic analysis of fisheries, Fishing New Books, 1993.
• R.M. May, Stability and complexity in model ecosystems, Princeton Univ. Press, Princeton, 1974.
• J-D. Opsomer and J.M. Conrad, An open access analysis of the northern anchovy fishery, J. Environ. Econ. Manage. 27 (1994), 2-37.
• M.L. Rosenzweig, Paradox of enrichment: Destabilization of exploitation ecosystem in ecological time, Science 171 (1971), 385-387.
• E. Sáez and E. González-Olivares, Dynamics of a predator-prey model, SIAM J. Appl. Math. 59 (1999), 1867-1878.
• M.B. Schaefer, Some aspects of the dynamics of population to the management of the commercial marine fisheries, Bull. Inter-Amer. Tropical Tuna Comm. 1 (1954), 27-56; Reprinted in Bull. Math. Biol. 53 (1991), 253-279.
• V.L. Smith, On models of commercial fishing, J. Polit. Econ. 77 (1969), 181-198.
• F. Takens, Unfoldings of certain singularities of vector fields, Generalized Hopf bifurcations, J. Differential Equations 14 (1973), 476-493.
• C.J. Walters, Adaptive management of renewable resources, Macmillan Publ. Co., New York, 1986.
• Wolfram Research, Mathematica: A system for doing mathematics by computer.