Biocontrol in an impulsive predator–prey model

Mathematical Biosciences - Tập 256 - Trang 102-115 - 2014
Alan J. Terry1
1Division of Mathematics, University of Dundee, Dundee DD1 4HN, UK

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