Biocontrol in an impulsive predator–prey model
Tài liệu tham khảo
http://www.mathworks.co.uk/products/matlab/.
Abrams, 2000, The nature of predation: prey dependent, ratio dependent or neither?, Trends Ecol. Evol., 15, 337, 10.1016/S0169-5347(00)01908-X
Bainov, 1993
Beddington, 1975, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol., 44, 331, 10.2307/3866
Beddington, 1976, The components of arthropod predation: II. The predator rate of increase, J. Animal Ecol., 45, 165, 10.2307/3773
Boukadida, 1994, The use of Encarsia formosa in integrated programs to control the whitefly Trialeurodes vaporariorum Westw. (Hom., Aleyrodidae) on greenhouse cucumber, J. Appl. Entomol., 118, 203, 10.1111/j.1439-0418.1994.tb00795.x
Caltagirone, 1989, The history of the vedalia beetle importation to California and its impact on the development of biological control, Annu. Rev. Entomol., 34, 1, 10.1146/annurev.en.34.010189.000245
Conner, 2003, Artificial selection: a powerful tool for ecologists, Ecology, 84, 1650, 10.1890/0012-9658(2003)084[1650:ASAPTF]2.0.CO;2
DeAngelis, 1975, A model for trophic interaction, Ecology, 56, 881, 10.2307/1936298
Deng, 2006, Equilibriumizing all food chain chaos through reproductive efficiency, Chaos, 16
Gao, 2011, The effects of impulsive releasing methods of natural enemies on pest control and dynamical complexity, Nonlinear Anal.: Hybrid Syst., 5, 540
Gourley, 2004, A stage structured predator–prey model and its dependence on maturation delay and death rate, J. Math. Biol., 49, 188, 10.1007/s00285-004-0278-2
Haque, 2011, A detailed study of the Beddington–DeAngelis predator–prey model, Math. Biosci., 234, 1, 10.1016/j.mbs.2011.07.003
Iooss, 1980
Kindlmann, 2003, Insect predator–prey dynamics and the biological control of aphids by ladybirds, 118
Lakshmikantham, 1989
Mailleret, 2006, Optimal release policy for prophylactic biological control, vol. 341, 89
Mailleret, 2009, Global stability and optimisation of a general impulsive biological control model, Math. Biosci., 221, 91, 10.1016/j.mbs.2009.07.002
Nie, 2009, Existence and stability of periodic solution of a predator–prey model with state-dependent impulsive effects, Math. Comput. Simul., 79, 2122, 10.1016/j.matcom.2008.11.015
Nundloll, 2010, Influence of intrapredatory interferences on impulsive biological control efficiency, Bull. Math. Biol., 72, 2113, 10.1007/s11538-010-9531-6
Nundloll, 2010, Two models of interfering predators in impulsive biological control, J. Biol. Dynam., 4, 102, 10.1080/17513750902968779
Orr, 2009, Biological control and integrated pest management, 207
Pang, 2009, Extinction and permanence in delayed stage-structure predator–prey system with impulsive effects, Chaos Solit. Fract., 39, 2216, 10.1016/j.chaos.2007.06.071
Phillips, 2006, Invasion and the evolution of speed in toads, Nature, 439, 10.1038/439803a
Sapoukhina, 2003, The role of prey taxis in biological control: a spatial theoretical model, Am. Natural., 162, 61, 10.1086/375297
Shah, 2003, Entomopathogenic fungi as biological control agents, Appl. Microbiol. Biotechnol., 61, 413, 10.1007/s00253-003-1240-8
Shi, 2008, Staged-structured Lotka–Volterra predator–prey models for pest management, Appl. Math. Comput., 203, 258, 10.1016/j.amc.2008.04.032
Shi, 2009, A predator–prey model with disease in the prey and two impulses for integrated pest management, Appl. Math. Modell., 33, 2248, 10.1016/j.apm.2008.06.001
Shulgin, 1998, Pulse vaccination strategy in the SIR epidemic model, Bull. Math. Biol., 60, 1123, 10.1016/S0092-8240(98)90005-2
Simons, 2006, Extinction criteria in stage-structured population models with impulsive culling, SIAM J. Appl. Math., 66, 1853, 10.1137/050637777
Skalski, 2001, Functional responses with predator interference: viable alternatives to the Holling type II model, Ecology, 82, 3083, 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2
Stern, 1959, The integrated control concept, Hilgardia, 29, 81, 10.3733/hilg.v29n02p081
Tang, 2010, Optimum timing for integrated pest management: modelling rates of pesticide application and natural enemy releases, J. Theor. Biol., 264, 623, 10.1016/j.jtbi.2010.02.034
A.J. Terry, Control of Pests and Diseases, Ph.D. thesis, University of Surrey, 2009.
Terry, 2010, Impulsive culling of a structured population on two patches, J. Math. Biol., 61, 843, 10.1007/s00285-009-0325-0
Terry, 2010, Pulse vaccination strategies in a metapopulation SIR model, Math. Biosci. Eng., 7, 457, 10.3934/mbe.2010.7.455
Terry, 2011, Dynamics of a structured population on two patches, J. Math. Anal. Appl., 378, 1, 10.1016/j.jmaa.2011.01.018
Terry, 2013, Prey resurgence from mortality events in predator–prey models, Nonlinear Anal.: Real World Appl., 14, 2180, 10.1016/j.nonrwa.2013.04.006
Terry, 2014, A predator–prey model with generic birth and death rates for the predator, Math. Biosci., 248, 57, 10.1016/j.mbs.2013.12.002
Turchin, 2003
Verdy, 2010, Modulation of predator–prey interactions by the Allee effect, Ecol. Modell., 221, 1098, 10.1016/j.ecolmodel.2010.01.005
Wang, 2010, The dynamics of an epidemic model for pest control with impulsive effect, Nonlinear Anal.: Real World Appl., 11, 1374, 10.1016/j.nonrwa.2009.02.027
Zhang, 2007, Impulsive control strategies for pest management, J. Biol. Syst., 15, 235, 10.1142/S0218339007002106
Zhang, 2008, On the impulsive controllability and bifurcation of a predator–pest model of IPM, BioSystems, 93, 151, 10.1016/j.biosystems.2008.03.008
Zwillinger, 1989