Analysis of predator-prey models with continuous threshold harvesting

Applied Mathematics and Computation

Volumn 217, Issue 12, 2011, Pages 5265-5278

  Leard, Benjamin ^a   Rebaza, Jorge ^b  

^a Department of Obstetrics Gynecology   (United States)

^b MISSOURI STATE UNIVERSITY   (United States)

Author keywords

Dynamical systems; Harvesting; Predator prey models; Threshold policy

Indexed keywords

BOUNDEDNESS OF SOLUTION; ECONOMIC CONSTRAINTS; HETEROCLINIC ORBIT; PERIODIC ORBITS; PREDATOR-PREY ECOSYSTEM; PREDATOR-PREY MODELS; STABILITY OF EQUILIBRIUM; THRESHOLD POLICIES; THRESHOLD POLICY;

DYNAMICAL SYSTEMS; ECOLOGY; HARVESTING; NUMERICAL ANALYSIS;

MAMMALS;

EID: 79551626246     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.11.050     Document Type: Article

References (17)

1. C.W. Clark Bioeconomics Modelling and Fisheries Management 1985 Wiley
2. C.W. Clark Mathematical Bioeconomics: The Optimal Management of Renewable Resources 2nd Edition 1990 Wiley-Interscience
3. L.W. Botsford, J.C. Castilla, and C.H. Peterson The management of fisheries and marine ecosystems Science 277 5325 1997 509 515
4. A.A. Rosenberg, M.J. Fogarty, M.P. Sissenwine, J.R. Beddington, and J.G. Shepherd Achieving sustainable use of renewable resources Science 262 5135 1993 828 829 New Series
5. J.S. Collie, P.D. Spencer, Management Strategies for fish populations subject to long term environmental variability and depensatory predation, Technical Report 93-02, Alaska Sea Grant College, 1993, pp. 629-650.
6. R. Lande, S. Engen, and B. Saether Optimal harvesting of fluctuating populations with a risk of extinction Am. Nat. 145 5 1995
7. R. Lande, B. Saether, and S. Engen Threshold harvesting for sustainability of fluctuating resources Ecology 78 5 1997 1341 1350
8. S. Aanes, S. Engen, B. Saether, T. Willebrand, and V. Marcstrom Sustainable harvesting strategies of willow ptarmigan in a fluctuating environment Ecol.Appl. 12 1 2002
9. M.E.M. Meza, A. Bhaya, Kaszkurewiczk, and M.I.S. Costa Threshold policies control for predator-prey systems using a control Liapunov function approach Theor. Popul. Biol. 67 2005 273 284
10. M.E.M. Meza, A. Bhaya, Kaszkureqick, Control of one and two species predator-prey models using continuous robust threshold policies, in:proceeding XIV Congresso Brasileiro de Automatica 2002.
11. B. Leard, C. Lewis, and J. Rebaza Dynamics or ratio-dependent predator-prey models with nonconstant harvesting Disc. Cont. Dynam. Syst. S 1 2008 303 315
12. D. Xiao, and L.S. Jennings Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting SIAM J. Appl. Math. 65 2005 737 753
13. J. Hale Ordinary Differential Equations 1980 John Wiley and Sons
14. B. Ermentrout Simulating analyzing and animating dynamical sytems SIAM 2002
15. L. Perko Differential Equations and Dynamical Systems Texts in Applied Mathematics vol. 7 2006 Springer-Verlag
16. L. Dieci, and J. Rebaza Point-to-periodic and periodic-to-periodic connections BIT Numer. Math. 44 2004 41 62
17. J. Rebaza Smooth Schur factorizations in the continuation of separatrices Lin. Alg. Appl. 421 2007 138 156