Citation: |
[1] |
F. Brauer and A. C. Soudack, Stability regions and transition phenomena for harvested predator-prey systems, J.Math.Biol., 7 (1979), 319-337.doi: 10.1007/BF00275152. |
[2] |
F. Brauer and A. C. Soudack, Stability regions in predator-prey systems with constant rate prey harvesting, J. Math. Biol., 8 (1979), 55-71.doi: 10.1007/BF00280586. |
[3] |
F. Brauer and A. C. Soudack, Coexistence properties of some predator-prey systems under constant rate harvesting and stocking, J. Math. Biol., 12 (1982), 101-114.doi: 10.1007/BF00275206. |
[4] |
F. Brauer and D. A. Sánchez, Periodic environments and periodic harvesting, Natural Resource Modeling, 16 (2003), 233-244.doi: 10.1111/j.1939-7445.2003.tb00113.x. |
[5] |
J. Chen, J. Huang, S. Ruan and J. Wang, Bifurcations of invariant tori in predator-prey models with seasonal prey harvesting, SIAM J. Appl. Math., 73 (2013), 1876-1905.doi: 10.1137/120895858. |
[6] |
J. P. Cohen and J. S. Foale, Sustaining small-scale fisheries with periodically harvested marine reserves, Marine Policy, 37 (2013), 278-287.doi: 10.1016/j.marpol.2012.05.010. |
[7] |
C. W. Clark, Mathematical Bioeconomics, The Optimal Management of Renewable Resources, $2^{nd}$ edition, John Wiley & Sons, New York -Toronto, 1990. |
[8] |
G. Dai and M. Tang, Coexistence region and global dynamics of a harvested predator-prey system, SIAM J. Appl. Math., 58 (1998), 193-210.doi: 10.1137/S0036139994275799. |
[9] |
R. M. Etoua and C. Rousseau, Bifurcation analysis of a generalissed Gause model with prey harvesting and a generalized Holling response function of type III, J. Differential Equations, 249 (2010), 2316-2356.doi: 10.1016/j.jde.2010.06.021. |
[10] |
M. Fan and K. Wang, Optimal harvesting policy for single population with periodic coefficients, Mathematical Biosciences, 152 (1998), 165-177.doi: 10.1016/S0025-5564(98)10024-X. |
[11] |
M. Hasanbulli , P. S. Rogovchenko and Y. V. Rogovchenko, Dynamics of a single species in a fluctuating environment under periodic yield harvesting, Journal of Applied Mathematics, Volume 2013, Article ID 167671, 12 pages. |
[12] |
L. S. Hill, J. E. Murphy, K. Reid, P. N. Trathan and J. A. Constable, Modelling Southern Ocean ecosystems: Krill, the food-web, and the impacts of harvesting, Biol. Rev., 81 (2006), 581-608. |
[13] |
M. Hirsch, S. Smale and R. Devaney, Differential Equations, Dynamical Systems and An Introduction to Chaos, Elsevier, New York, 2004.doi: 10.1007/978-1-4612-0873-0. |
[14] |
S.-B. Hsu and X.-Q. Zhao, A Lotka-Volterra competition model with seasonal succession, J. Math. Biol., 64 (2012), 109-130.doi: 10.1007/s00285-011-0408-6. |
[15] |
S. S. Hu and A. J. Tessier, Seasonal succession and the strength of intra- and interspecific competition in a Daphnia assemblage, Ecology, 76 (1995), 2278-2294.doi: 10.2307/1941702. |
[16] |
B. Leard, C. Lewis and J. Rebaza, Dynamics of ratio-depedent predator-prey models with nonconstant harvesting, Discrete Contin. Dynam. Syst. Ser. S 1 (2008), 303-315.doi: 10.3934/dcdss.2008.1.303. |
[17] |
R. May, J. R. Beddington, C. W. Clark, S. J. Holt and R. M. Laws, Management of multispecies fisheries, Science, 205 (1979), 267-277.doi: 10.1126/science.205.4403.267. |
[18] |
M. B. Schaefer, Some aspects of the dynamics of populations important to the management of commercial marine fisheries, Bull. Inter-Am. Trop. Tuna Comm., 1 (1954), 25-56. |
[19] |
R. J. Schmitt and S. J. Holbrook, Seasonally fluctuating resources and temporal variability of interspecific competition, Oecologia, 69 (1986), 1-11.doi: 10.1007/BF00399030. |
[20] |
Y. L. Tang and D. Xiao, Periodic solutions for a predator-prey model with periodic harvesting rate, International Journal of Bifurcation and Chaos, 24 (2014), 1450096(12 pages).doi: 10.1142/S0218127414500965. |
[21] |
C. J. Waiters and P. J. Bandy, Periodic harvest as a method of increasing big game yields, J. Wildl. Manage., 36 (1972), 128-134. |
[22] |
D. Xiao and L. Jennings, Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting, SIAM J. Appl. Math., 65 (2005), 737-753.doi: 10.1137/S0036139903428719. |
[23] |
D. Xiao, W. Li and M. Han, Dynamics in a ratio-dependent predator-prey model with predator harvesting, J. Math. Anal. Appl., 324 (2006), 14-29.doi: 10.1016/j.jmaa.2005.11.048. |
[24] |
C. Xu, M. S. Boyce and D. J. Daley, Harvesting in seasonal environments, Journal of Mathematical Biology, 50 (2005), 663-682.doi: 10.1007/s00285-004-0303-5. |