Continuous Threshold Prey Harvesting in Predator-Prey Models
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32795
Continuous Threshold Prey Harvesting in Predator-Prey Models

Authors: Jonathan Bohn, Jorge Rebaza, Kaitlin Speer


The dynamics of a predator-prey model with continuous threshold policy harvesting functions on the prey is studied. Theoretical and numerical methods are used to investigate boundedness of solutions, existence of bionomic equilibria, and the stability properties of coexistence equilibrium points and periodic orbits. Several bifurcations as well as some heteroclinic orbits are computed.

Keywords: Predator-prey models, threshold harvesting, dynamicalsystems

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2254


[1] T. M. Asfaw, Dynamics of generalized time dependent predator prey model with nonlinear harvesting, Int. J. Math. Anal. 3 (2009), 1473- 1485.
[2] B. Ermentrout, Stimulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students, SIAM (2002).
[3] J. Hale, Ordinary Differential Equations, J. Wiley & Sons (1980).
[4] J. Hale, H. Koc┬©ak, Dynamics and Bifurcations, Springer Verlag (1991).
[5] L. Ji, C. Wu, Qualitative analysis of a predator-prey model with constantrate prey harvesting incorporating a constant prey refuge, Nonl Anal: Real World Appl. (2009) doi:10.1016/j.nonrwa.2009.07.003.
[6] T. K. Kar, Modelling and analysis of a harvested prey-predator system incorporating a prey refuge, J. Comp. & Appl. Math. 185 (2006), 19-33.
[7] B. Leard, C. Lewis, J. Rebaza, Dynamics of ratio-dependent of predatorprey models with nonconstant harvesting, Disc. & Cont. Dynam. Syst. S 1 (2008), 303-315.
[8] Y. Li and J. Muldowney, On Bendixon-s criterion, J. Diff. Equat. 106 (1993), 27-39.
[9] M. E. M. Meza, A. Bhaya, Kaszkurewiczk, M. I. S. Costa, Threshold policies control for predator-prey systems using a control Liapunov function approach. Theoretical Population Biology, 67 (2005), 273-284.
[10] D. Xiao, W. Li and M. Han, Dynamics in a ratio-dependent predatorprey model with predator harvesting, J. Math Anal. Appl. 324 (2006), 14-29.