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Articles

Effects of pesticide dose on Holling II predator–prey model with feedback control

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Pages 527-550 | Received 17 Oct 2017, Accepted 15 May 2018, Published online: 04 Jun 2018

References

  • D. Bainov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman, Harlow, Vol. 66, 1993.
  • S. Blower and H. Dowlatabadi, Sensitivity and uncertainty analysis of complex-models of disease transmission? An HIV model, as an example, Int. Stat. Rev. 62 (1994), pp. 229–243.
  • K. Ciesielski, On time reparametrizations and isomorphisms of impulsive dynamical systems, Ann. Polon. Math. 84 (2004), pp. 1–25.
  • C.J. Dai, M. Zhao and L.S. Chen, Homoclinic bifurcation in semi-continuous dynamic systems, Int. J. Biomath. 05 (2012), 1250059, 19 pages.
  • R. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, New York, 1989.
  • A.F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer Academic, Dordrecht, 1988.
  • M.Z. Huang, J.X. Li, X.Y. Song and H.J. Guo, Modeling impulsive injections of insulin: towards artificial pancreas, SIAM J. Appl. Math. 72 (2012), pp. 1524–1548.
  • S.U. Karaagac, Insecticide Resistance, InTech Press, London, 2012.
  • S. Kaul, On impulsive semidynamical systems, J. Math. Anal. Appl. 150 (1990), pp. 120–128.
  • Y. Kuang and H.I. Freedman, Uniqueness of limit cycles in Gause-type models of predator–prey systems, Math. Biosci. 88 (1988), pp. 67–84.
  • T. Li and J. Yorke, Period three implies chaos, Amer. Math. 82 (1975), pp. 985–992.
  • J.H. Liang, S.Y. Tang, R.A. Cheke and J.H. Wu, Adaptive release of natural enemies in a pest-natural enemy system with pesticide resistance, Bull. Math. Biol. 75 (2013), pp. 2167–2195.
  • X.N. Liu and L.S. Chen, Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator, Chaos Solitons Fractals 16 (2003), pp. 311–320.
  • B. Liu, Z.D. Teng and L.S. Chen, Analysis of a predator–prey model with Holling II functional response concerning impulsive control strategy, J. Comput. Appl. Math. 193 (2006), pp. 347–362.
  • B. Liu, Y. Tian and B.L. Kang, Dynamics on a Holling II predator–prey model with state-dependent impulsive control, Int. J. Biomath. 5 (2012), 18 pages.
  • Y. Liu, X. Zhang and T. Zhou, Multiple periodic solutions of a delayed predator–prey model with non-monotonic functional response and stage structure, J. Biol. Dyn. 8(1) (2014), pp. 145–160.
  • Y. Lv, R. Yuan and Y. Pei, Two types of predator–prey models with harvesting: non-smooth and non-continuous, J. Comput. Appl. Math. 250 (2013), pp. 122–142.
  • S. Marino, I.B. Hogue, C.J. Ray and D.E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol. 254 (2008), pp. 178–196.
  • M.D. McKay, R.J. Beckman and W.J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics. 21 (1979), pp. 239–245.
  • J.C. Panetta, A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment, Bull. Math. Biol. 58 (1996), pp. 425–447.
  • W.J. Qin, S.Y. Tang and R.A. Cheke, The effects of resource limitation on a predator–prey model with control measures as nonlinear pulses, Math. Probl. Eng. 2014 (2014), 14pages.
  • P. Simeonov and D. Bainov, Orbital stability of periodic solutions of autonomous systems with impulsive effect, Int. J. Systems Sci. 19 (1988), pp. 2561–2585.
  • K.B. Sun, T.H. Zhang and Y. Tian, Theoretical study and control optimization of an integrated pest management predator–prey model with power growth rate, Math. Biosci. 279 (2016), pp. 13–26.
  • S.Y. Tang and R.A. Cheke, Models for integrated pest control and their biological implications, Math. Biosci. 215 (2008), pp. 115–125.
  • S.Y. Tang, Y.N. Xiao and R.A. Cheke, Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak, Theor. Popul. Biol. 73 (2008), pp. 181–197.
  • S.Y. Tang, Y.N. Xiao and R.A. Cheke, Effects of predator and prey dispersal on success or failure of biological control, Bull. Math. Biol. 71 (2009), pp. 2025–2047.
  • S.Y. Tang, Y.N. Xiao and R.A. Cheke, Dynamical analysis of plant disease models with cultural control strategies and economic thresholds, Math. Comput. Simulat. 80 (2010), pp. 894–921.
  • S.Y. Tang, W.H. Pang, R.A. Cheke and J.H. Wu, Global dynamics of a state-dependent feedback control system, Adv. Differ. Equ. 2015 (2015), pp. 322.
  • S.Y. Tang, B. Tang, A.L. Wang and Y.N. Xiao, Holling II predator–prey impulsive semi-dynamic model with complex Poincaré map, Nonlinear Dynam. 81 (2015), pp. 1575–1596.
  • S.Y. Tang, Y.N. Xiao and J.H. Wu, Media impact switching surface during an infectious disease outbreak, Sci. Rep. 5 (2015), pp. 672.
  • M.B. Thomas, Ecological approaches and the development of truly integrated pest management, Proc. Natl. Acad. Sci. 96 (1999), pp. 5944–5951.
  • V.I. Utkin, J. Guldner and J.X. Shi, Sliding Mode Control in Electro-mechanical Systems, 2nd ed., Taylor & Francis Group, Boca Raton, 2009.
  • J.C. Van Lenteren and J. Woets, Biological and integrated pest control in greenhouses, Annu. Rev. Entomol. 33 (1988), pp. 239.
  • Y.P. Wang, M. Zhao, X.H. Pan and C.J. Dai, Dynamic analysis of a phytoplankton-fish model with biological and artificial control, Discrete Dyn. Nat. Soc. 2014 (2014). doi:doi: 10.1155/2014/914647.
  • J. Yang and S.Y. Tang, Holling type II predator–prey model with nonlinear pulse as state-dependent feedback control, J. Comput. Appl. Math. 291 (2016), pp. 225–241.
  • J. Yang, S.Y. Tang and Y.S. Tan, Complex dynamics and bifurcation analysis of host-parasitoid models with impulsive control strategy, Chaos Soliton. Fract. 91 (2016), pp. 522–532.
  • J. Yang, G.Y. Tang and S.Y. Tang, Modelling the regulatory system of a chemostat model with a threshold window, Math. Comput. Simulat. 132 (2017), pp. 220–235.
  • T.Q. Zhang, W.B. Ma, X.Z. Meng and T.H. Zhang, Periodic solution of a prey–predator model with nonlinear state feedback control, Appl. Math. Comput. 266 (2015), pp. 95–107.