Butterfly catastrophe model for wheat aphid population dynamics: Construction, analysis and application

Aheer, 2007, Impact of weather factors on population of wheat aphids at Mandi Baha-ud-Din district, J. Agric. Res., 45, 61 Aheer, 2008, Abiotic factors effect on population fluctuation of alate aphids in wheat, J. Agric. Res., 46, 367 Aheer, 1994, Role of weather in fluctuating aphid density in wheat crop, J. Agric. Res., 32, 295 Anne, 2010, Evolutionary ecology of the interactions between aphids and their parasitoids, C.R. Biol., 333, 554, 10.1016/j.crvi.2010.03.010 Arnold, 1984 Ashfaq, 2007, Role of abiotic factors in population fluctuation of aphids on wheat, Pak. Entomol., 29, 117 Brauer, 2010 Cui, 1982, Study on models of single populations: an expansion of the logistic and exponential equations, J. Theor. Biol., 98, 645, 10.1016/0022-5193(82)90143-6 Jones, 1977, Catastrophe theory applied to ecological systems, Simulation, 29, 1, 10.1177/003754977702900102 Dixon, 1987, Cereal aphids as an applied problem, Agric. Zool. Rev., 2, 1 Deakin, 1980, Applied catastrophe theory in the social and biological sciences, Bull. Math. Biol., 42, 647, 10.1007/BF02460985 Emilio, 2014, Aphid-plant interactions: a review, J. Plant Interact., 3, 223 Freier, 2007, The potential of predators in natural control of aphids in wheat: results of a ten-year field study in two German landscapes, BioControl, 52, 775, 10.1007/s10526-007-9081-5 Glimore, 1981 Kindlmann, 2010 Leslie, 2009, Population dynamics of cereal aphids: influence of a shared predator and weather, Agric. For. Entomol., 11, 73, 10.1111/j.1461-9563.2008.00405.x Li, 2012, Population dynamics of insect pests of butterfly catastrophe model and analysis, J. Northwest A&F Univ. (Nat. Sci. Ed.), 40, 103 Li, 1997, A self-adaptive model of population growth and its parameter estimation, Acta Ecol. Sin., 17, 311 Ling, 1987 Loehle, 1989, Catastrophe theory in ecology: a critical review and an example of the butterfly catastrophe, Ecol. Modell., 49, 125, 10.1016/0304-3800(89)90047-1 May, 1977, Thresholds and breakpoints in ecosystems with a multiplicity of stable states, Nature, 269, 471, 10.1038/269471a0 Ma, 2009, An approach to the nonlinear dynamics of Russian wheat aphid population growth with the cusp catastrophe model, Entomol. Res., 39, 175, 10.1111/j.1748-5967.2009.00216.x Nasir, 2001, Correlation between wheat aphid population and abiotic factors, Pak. Entomol., 23, 23 Owain, 2008, Insecticide resistance and implications for future aphid management in Australian grains and pastures: a review, Aust. J. Exp. Agric., 48, 1523, 10.1071/EA07426 Piyaratne, 2013, APHIDSim: a population dynamics model for wheat aphids based on swallowtail catastrophe theory, Ecol. Modell., 253, 9, 10.1016/j.ecolmodel.2012.12.032 Rosser, 2007, The rise and fall of catastrophe theory application in economics: was the baby thrown out with the bathwater?, J. Econ. Dyn. Control, 31, 3255, 10.1016/j.jedc.2006.09.013 Ran, 1985, An investigation on the effectiveness of aphidophagous natural enemies in cotton field, J. Northwest A&F Univ. (Nat. Sci. Ed.), 1, 14 Roopnarine, 2008, Ecological informatics: catastrophe theory Smith, 1963, Population dynamics in Daphnia magna and a new model for population growth, Ecology, 44, 651, 10.2307/1933011 Swartz, 1975, Discussion of parameter estimation in biological modeling: algorithms for estimation and evaluation of the estimates, J. Math. Biol., 1, 241, 10.1007/BF01273746 Stewart, 1982, Catastrophe theory in physics, Rep. Prog. Phys., 45, 185, 10.1088/0034-4885/45/2/002 Susana, 2009, Predation by Coccinella undecimpunctata L. (Coleoptera: Coccinellidae) on Myzus persicae Sulzer (Homoptera: Aphididae) effect of prey density, Biol. Control, 50, 25, 10.1016/j.biocontrol.2009.01.020 Saunders, 1980 Tomar, 2010, Impact of weather parameters on aphid population in cotton, Indian J. Agric. Res., 44, 125 Varah, 1982, A spline least squares method for numerical parameter estimation in differential equations, SIAM J. Sci. Comput., 3, 28, 10.1137/0903003 Wei, 2009, Analysis of pest population dynamics model using swallowtail catastrophe theory, Acta Ecol. Sin., 29, 5478 Wains, 2008, Aphid dynamics in wheat as affected by weather and crop planting time, J. Agric. Res., 46, 361 Yang, 1990, Temperature and light's effect for the growth of wheat aphids, Acta Agric. Univ. Henan., 24, 11 Zeeman, 1977 Zhao, 1991, Study on the cusp catastrophe model, sudden change region and controlling target during strategy of wheat aphid control, Syst. Eng., 9, 30 Zhao, 1989, Application of catastrophe theory to the management of wheat ecosystem, Chin. Sci. Bull., 22, 1745 Zhao, 1993, Catastrophe theory and application of some main pest in agriculture, Acta Agric. Boreali-Occident. Sin., 2, 48 Zhao, 2005, Catastrophe analysis of a predator model with prey, J. Northwest A&F Univ. (Nat. Sci. Ed.), 33, 65 Zhao, 1993, Cusp mutation model of cotton seedling aphids and its analysis, Chin. J. Ecol., 12, 62