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Journal of Applied Mathematics and Computing

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06-05-2016 | Original Research

Dynamical analysis of a new microbial pesticide model with the Monod growth rate

Authors: Tieying Wang, Yan Wang, Feng Liu

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2017

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Abstract

In this paper, a new mathematical model for the entomopathogenic nematode with the Monod growth rate is formulated. Firstly, continuous release of the entomopathogenic nematode is considered. The existence of limit cycles, the Hopf bifurcation and the stability of the periodic solution created by the bifurcation are proved. The sufficient conditions for the globally asymptotical stability of system are obtained. Secondly, impulsive release of the entomopathogenic nematode is also considered. By using the Floquet’s theorem and the small amplitude perturbations, we show that the pest-free periodic solution is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations. Thus, we provide mathematical evidence on how to release the entomopathogenic nematode in order to control pests at acceptably low levels.

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Bainov, D.D., Simeonov, P.S.: Impulsive Differential Equations: Periodic Solutions and Applications. Longman Scientific and Technical Press, Harlow (1993)MATH

Jiao, J.J., Cai, S.H., Chen, L.S.: Dynamical behaviors of a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators. J. Appl. Math. Comput. 35(1), 483–495 (2011)MathSciNetCrossRefMATH

Kepenekci, I., Hazir, S., Ozdem, A.: Evaluation of native entomopathogenic nematodes for the control of the European cherry fruit fly Rhagoletis cerasi L. (Diptera: Tephritidae) larvae in soil. Turk. J. Agric. For. 39, 74–79 (2015)CrossRef

Kulev, G.K., Bainov, D.D.: On the asymptotic stability of systems with impulses by the direct method of Lyapunov. J. Math. Anal. Appl. 140(2), 324–340 (1989)MathSciNetCrossRefMATH

Lacey, L.A., Georgis, R.: Entomopathogenic nematodes for control of insect pests above and below ground with comments on commercial production. J. Nematol. 44(2), 218–225 (2012)

Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)CrossRefMATH

Magalhaes, G.O., Vacari, A.M., Laurentis, V.L., De Bortoli, S.A., Polanczyk, R.A.: Interactions of Bacillus thuringiensis bioinsecticides and the predatory stink bug Podisus nigrispinus to control Plutella xylostella. J. Appl. Entomol. 139(1–2), 123–133 (2015)CrossRef

Meng, X.Z., Liu, R., Zhang, T.H.: Periodic solution of a pest management Gompertz model with impulsive state feedback control. Nonlinear Dyn. 78(2), 921–938 (2014)MathSciNetCrossRefMATH

Meng, X.Z., Wu, Z.T., Zhang, T.Q.: The dynamics and therapeutic strategies of a SEIS epidemic model. Int. J. Biomath. 6(5), 41–58 (2013)MathSciNetCrossRefMATH

10.

Meng, X.Z., Liu, R., Zhang, T.H.: Adaptive dynamics for a non-autonomous Lotka-Volterra model with size-selective disturbance. Nonlinear Anal. Real World Appl. 16, 202–213 (2014)MathSciNetCrossRefMATH

11.

Pilyugin, S.S., Waltman, P.: Multiple limit cycles in the chemostat with variable yield. Math. Biosci. 182(2), 151–166 (2003)MathSciNetCrossRefMATH

12.

Simeonov, P.S., Bainov, D.D.: Stability with respect to part of the variables in system with impulsive effect. J. Math. Anal. Appl. 117(1), 247–263 (1986)MathSciNetCrossRefMATH

13.

Sun, X.L.: History and current status of development and use of viral insecticides in China. Viruses 7(1), 306–319 (2015)CrossRef

14.

Singh, S.P., Yadav, A.K., Vardhan, S., Tripathi, C.P.M.: Diversity analysis of entomopathogenic nematodes against Helicoverpa armigera (Hbner) from Tarai region of IGP, India. Curr. Life Sci. 1, 15–23 (2015)

15.

Windley, M.J., Herzig, V., Dziemborowicz, S.A., Hardy, M.C., King, G.F., Nicholson, G.M.: Spider-venom peptides as bioinsecticides. Toxins 4(3), 191–227 (2012)CrossRef

16.

Yao, Z.J.: Almost periodic solution of Nicholson’s blowflies model with linear harvesting term and impulsive effects. Int. J. Biomath. 8(3), 255–272 (2015)MathSciNetCrossRefMATH

17.

Yao, Z.J.: Dynamic behaviors of n-species impulsive competitive system. Int. J. Nonlinear Sci. Numer. 15(6), 347–363 (2014)MathSciNetCrossRef

18.

Zhang, J.Y.: Geometrical Theory and Bifurcation Problem in Ordinary Differential Equations. Peking University Press, Beijing (1987)

19.

Zhang, Z.F., Ding, T.R., Huang, W.Z., Dong, Z.X.: Qualitative Theory of Differential Equations (Translations of Mathematical Monographs). American Mathematics Society, Providence (1992)

20.

Zolfagharian, M., Saeedizadeh, A., Abbasipour, H., Jooyandeh, A., Yazdi, A.A.: Efficacy of entomopathogenic nematode, Steinernema carpocapsaeagainst the diamondback moth, Plutella xylostella(L.) in laboratory condition. Arch. Phytopathol. Plant Prot. 48(5), 393–399 (2014)CrossRef

Title: Dynamical analysis of a new microbial pesticide model with the Monod growth rate
Authors: Tieying Wang
Yan Wang
Feng Liu
Publication date: 06-05-2016
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2017
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-016-1012-0

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