Global analysis of a delayed density dependent predator–prey model with Crowley–Martin functional response

Jai Prakash Tripathi1,2, Swati Tyagi1, Syed Abbas1
1School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, H.P. 175001, India
2Department of Mathematics, Central University of Rajasthan, NH-8, Bandarsindri, Kishangarh 305801, Distt.-Ajmer, Rajasthan, India

Tài liệu tham khảo

Berryman, 1992, The origin and evolution of predator–prey theory, Eco Soc Am, 73, 1530 Ruan, 2001, Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J Appl Math, 61, 1445, 10.1137/S0036139999361896 Abbas, 2010, Existence, uniqueness and stability analysis of allelopathic stimulatory phytoplankton model, J Math Anal Appl, 367, 249, 10.1016/j.jmaa.2010.01.024 Bazykin, 1998, Nonlinear dynamics of interacting populations, World Sci Kratina, 2009, Functional responses modified by predator density, Oecologia, 159, 425, 10.1007/s00442-008-1225-5 Haiyin, 2011, Dynamics of the density dependent predator–prey system with Bedinton–DeAngelis functional response, J Math Anal Appl, 374, 644, 10.1016/j.jmaa.2010.08.029 Abbas, 2012, Almost periodic solution of a non-autonomous model of phytoplankton allelopathy, Nonlinear Dyn, 67, 203, 10.1007/s11071-011-9972-y Anderson, 2001, Predator responses, prey refuges, and density-dependent mortality of a marine fish, Ecology, 82, 245, 10.1890/0012-9658(2001)082[0245:PRPRAD]2.0.CO;2 Bairagi, 2007, Role of infection on the stability of a predator-prey system with several response functions – a comparative study, J Theor Biol, 248, 10, 10.1016/j.jtbi.2007.05.005 Upadhyay, 2009, Dynamics of three species food chain model with Crowley–Martin type functional response, Chaos, Solit Fract, 42, 1337, 10.1016/j.chaos.2009.03.020 Sklaski, 2001, Functional responses with predator interference: viable alternative to Holling type II model, Ecology, 82, 3083, 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2 Upadhyay, 2010, Dynamic complexities in a tri-trophic food chain model with Holling type II and Crowley–Martin functional response, Nonlinear Anal: Model Control, 15, 361, 10.15388/NA.15.3.14331 Crowley, 1989, Functional responses and interference within and between year classes of a dragonfly population, J N Am Benth Soc, 8, 211, 10.2307/1467324 Dong, 2013, The asymptotic behaviour of a chemostat model with Crowley–Martin type functional response and time delays, J Math Chem, 51, 1231, 10.1007/s10910-012-0138-z Tripathi, 2014, Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge, Nonlinear Dyn, 80, 177, 10.1007/s11071-014-1859-2 Lv, 2013, A prey-predator model with harvesting for fishery resource with prey reserve area, Appl Math Model, 37, 3048, 10.1016/j.apm.2012.07.030 Perc, 2007, Noise-guided evolution within cyclical interactions, New J Phys, 267, 10.1088/1367-2630/9/8/267 Perc, 2007, Cyclical interactions with alliance-specific heterogeneous invasion rates, Phys Rev E, 75, 052102, 10.1103/PhysRevE.75.052102 Szolnoki, 2014, Cyclic dominance in evolutionary games: a review, J R Soc Interface, 100, 20140735, 10.1098/rsif.2014.0735 Perc, 2013, Collective behavior and evolutionary games - an introduction, Chaos, Solit Fract, 56, 1, 10.1016/j.chaos.2013.06.002 Castellano, 2009, Statistical physics of social dynamics, Rev Modern Phys, 81, 591, 10.1103/RevModPhys.81.591 Szolnoki, 2013, Correlation of positive and negative reciprocity fails to confer an evolutionary advantage:phase transitions to elementary strategies, Phys Rev X, 3, 041021 Szolnoki, 2012, Defense mechanisms of empathetic players in the spatial ultimate game, Phys Rev Lett, 109, 078701, 10.1103/PhysRevLett.109.078701 Szolnoki, 2010, Reward and cooperation in the spatial public good game, Lett J Exploring Front Phys, 92, 38003 Cantrell, 2001, On the dynamics of predator–prey models with the Beddington–DeAngelis functional response, J Math Anal Appl, 257, 206, 10.1006/jmaa.2000.7343 Freedman, 1980 Brikhoff, 1982 Aziz-Alaoui, 2003, Boundedness and global stability for a predator–prey model with modified Leslie–Gower and Holling-type II schemes, Appl Math Lett, 16, 1069, 10.1016/S0893-9659(03)90096-6 Oaten, 1975, Functional response and stability in predator–prey systems, Am Nat, 109, 289, 10.1086/282998 Perko, 2001 Freedman, 1984, Persistence in models of three interacting predator–prey populations, Math Biosci, 68, 213, 10.1016/0025-5564(84)90032-4 Tripathi, 2012, Stability analysis of two prey one predator model, AIP Conf Proc, 1479, 905, 10.1063/1.4756288 Lotka, 1956 DeAngelis, 1975, A model for tropic interaction, Ecology, 56, 881, 10.2307/1936298 Sarwardi, 2014, Persistence and global stability of Baazykin predator-prey model with Beddington–DeAngelis response function, Commun Nonlinear Sci Numer Simulat, 19, 189, 10.1016/j.cnsns.2013.05.029 Tripathi, 2014, Local and global stability analysis of two prey one predator model with help, Commun Nonlinear Sci Numer Simulat, 19, 3284, 10.1016/j.cnsns.2014.02.003 Haque, 2011, A detailed study of the Beddington–DeAngelis predator-prey model, Math Biosci, 234, 1, 10.1016/j.mbs.2011.07.003 Bereta, 1998, Global analysis in some delayed ratio dependent predator–prey systems, Nonlin Anal TMA, 32, 381, 10.1016/S0362-546X(97)00491-4 Kuang, 1993 Hsu, 2001, Global analysis of the Michaelis–Menten-type ratio-dependent predator–prey system, J Math Biol, 42, 489, 10.1007/s002850100079 Liu, 2006, A stage-structured predator–prey model of Bedington–DeAngelis type, SIAM J Appl Math, 66, 1101, 10.1137/050630003 Liu, 2010, Predator–prey model of Bedington–DeAngelis type with maturation and gestation delays, Nonlinear Anal RWA, 11, 4072, 10.1016/j.nonrwa.2010.03.013 Annik, 2001, Predator–prey models with delay and prey harvesting, J Math Biol, 43, 247, 10.1007/s002850100095 Butler, 1986, Uniformly persistent systems, Proc Am Math Soc, 96, 425, 10.1090/S0002-9939-1986-0822433-4 Hassell, 1971, Mutual interference between searching insect parasites, J Anim Ecol, 40, 473, 10.2307/3256 Tripathi, 2015, A density dependent delayed predator-prey model with Beddington–DeAngelis type function response incorporating a prey refuge, Commun Nonlinear Sci Numer Simulat, 22, 427, 10.1016/j.cnsns.2014.08.018 Hassard, 1981, Theory and application of Hopf bifurcation, CUP Arch Chen, 2007, Dynamic behaviours of a delay differential equation model of plankton allelopathy, J Comput Appl Math, 206, 733, 10.1016/j.cam.2006.08.020 Song, 2001, Optimal harvesting and stability with stage-structure for a two species competitive system, Math Biosci, 170, 173, 10.1016/S0025-5564(00)00068-7 Gopalsamy, 1992 Levin, 1977, A more functional response to predator–prey stability, Am Nat, 111, 381, 10.1086/283170 Freedman, 1983, The trade-off between mutual interference and time lags in predator–prey systems, Bull Math Biol, 45, 991, 10.1007/BF02458826 Hale, 1993