
Mathematical Biosciences and Engineering, 2019, 16(6): 79637981. doi: 10.3934/mbe.2019401.
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Optimization of an integrated feedback control for a pest management predatorprey model
1 College of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
2 College of Foreign Languages, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
Received: , Accepted: , Published:
Special Issues: Nonsmooth biological dynamical systems and applications
Keywords: semicontinuous dynamic systems; order1 periodic solution; successor functions; limit cycle; optimization
Citation: Zhenzhen Shi, Huidong Cheng, Yu Liu, Yanhui Wang. Optimization of an integrated feedback control for a pest management predatorprey model. Mathematical Biosciences and Engineering, 2019, 16(6): 79637981. doi: 10.3934/mbe.2019401
References:
 1. H. Guo and X. Song, An impulsive predatorprey system with modified LeslieGower and Holling type Ⅱ schemes, Chaos Solitons Fract., 36 (2008), 1320–1331.
 2. R. Kooij, J. Arus and A. Embid, Limit cycles in the HollingTanner model, Publicacions Matematiques, 41 (1997), 149–167.
 3. E. Saez and E. GonzalezOlivares, Dynamics of a predatorprey model, Siam J. Appl. Math., 59 (1999), 1867–1878.
 4. F. Zhu, X. Meng and T. Zhang, Optimal harvesting of a competitive nspecies stochastic model with delayed diffusions, Math. Biosci. Eng., 16 (2019), 1554–1574.
 5. Y. Li, Y. Li, Y. Liu, et al., Stability analysis and control optimization of a preypredator model with linear feedback control, Discrete Dyn. Nature Soc., 2018 (2018), 4945728.
 6. C. Li and S. Tang, Analyzing a generalized pestnatural enemy model with nonlinear impulsive control, Open Math., 16 (2018), 1390–1411.
 7. J. Gu, Y. Zhang and H. Dong, Dynamic behaviors of interaction solutions of (3+1)dimensional shallow water wave equation, Comput. Math. Appl., 76 (2018), 1408–1419.
 8. Z. Shi, J. Wang, Q. Li, et al., Control optimization and homoclinic bifurcation of a preypredator model with ratiodependent, Adv. Differ. Equ., 2019 (2019), 2.
 9. Y. Tian, S. Tang and R. A. Cheke, Nonlinear statedependent feedback control of a pestnatural enemy system, Nonlinear Dyn., 94 (2018), 2243–2263.
 10. Y. Li, H. Cheng, J. Wang, et al, Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy, Adv. Differ. Equ., 2018 (2018), 32.
 11. T. Zhang, Y. Song, T. Zhang, et al, A stagestructured predatorprey SI model with disease in the prey and impulsive effects, Math. Model. Anal., 18 (2013), 505–528.
 12. Z. Shi, Y. Li and H. Cheng, Dynamic analysis of a pest management smith model with impulsive state feedback control and continuous delay, Mathematics, 7 (2019), 591.
 13. Z. Jiang, X. Bi, T. Zhang, et al., Global hopf bifurcation of a delayed phytoplanktonzooplankton system considering toxin producing effect and delay dependent coefficient, Math. Biosci. Eng., 16 (2019), 3807–3829.
 14. Y. Li, H. Cheng and Y. Wang, A Lycaon pictus impulsive state feedback control model with Allee effect and continuous time delay, Adv. Differ. Equ., 2018 (2018), 367.
 15. K. Liu, T. Zhang and L. Chen, Statedependent pulse vaccination and therapeutic strategy in an SI epidemic model with nonlinear incidence rate, Comput. Math. Method. M., 2019 (2019), article ID 3859815.
 16. F. Wang, B. Chen, Y. Sun, et al., Finite time control of switched stochastic nonlinear systems, Fuzzy Set. Syst., 35 (2019), 140–152.
 17. S. Tang, X. Tan, J. Yang, et al., Periodic solution bifurcation and spiking dynamics of impacting predatorprey dynamical model, Int. J. Bifurcat. Chaos, 28 (2018), 1850147.
 18. G. Pang and L. Chen, Periodic solution of the system with impulsive state feedback control, Nonlinear Dyn., 78 (2014), 743–753.
 19. Z. Zhao, L. Pang and X. Song, Optimal control of phytoplankton fish model with the impulsive feedback control, Nonlinear Dyn., 88 (2017), 2003–2011.
 20. Y. Gong and J. Huang, Bogdanovtakens bifurcation in a LeslieGower predatorprey model with prey harvesting, Acta Math. Appl. SinE, 30 (2014), 239–244.
 21. T. Zhang, X. Meng and Y. Song, The dynamics of a highdimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments, Nonlinear Dyn., 64 (2011), 1–12.
 22. J. Jiao, L. Chen, J. Nieto, et al., Permanence and global attractivity of stagestructured predatorprey model with continuous harvesting on predator and impulsive stocking on prey, Appl. Math. Mech., 195 (2008), 316–325.
 23. Y. Pei, C. Li and L. Chen, Continuous and impulsive harvesting strategies in a stagestructured predatorprey model with time delay, Math. Comput. Simulat., 79 (2009), 2994–3008.
 24. J. Jiao, S. Cai and L. Li, Dynamics of a periodic switched predatorprey system with impulsive harvesting and hibernation of prey population, J. Franklin I., 353 (2016), 3818–3834.
 25. K. Sun, T. Zhang and Y. Tian, Dynamics analysis and control optimization of a pest management predatorprey model with an integrated control strategy, Appl. Math. Comput., 292 (2017), 253–271.
 26. S. Tang and L. Chen, Global attractivity in a foodlimited population model with impulsive effects, J. Math. Anal. Appl., 292 (2004), 211–221.
 27. R. N. Guedes, G. Smagghe, J. D. Stark, et al., Pesticideinduced stress in arthropod pests for optimized integrated pest management programs, Ann. Rev. Entomol., 61 (2015), 43.
 28. P. H. Leslie, Some further notes on the use of matrices in population mathematics, Biometrika, 35 (1948), 213–245.
 29. F. Liu, Q. Xue and K. Yabuta, Boundedness and continuity of maximal singular integrals and maximal functions on triebellizorkin spaces, Sci. ChinaMath., Mathematics, Doi: 10.1007/s1142501794165.
 30. J. Wang, H. Cheng, X. Meng, et al., Geometrical analysis and control optimization of a predatorprey model with multi statedependent impulse, Adv. Differ. Equ., 2017 (2017), 252.
 31. W. Lv and W. Fang, Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks, Adv. Differ. Equ., 2017 (2017), 374.
 32. Z. Zhao, Z. Li and L. Chen, Existence and global stability of periodic solution for impulsive predatorprey model with diffusion and distributed delay, J. Appl. Math. Comput., 33 (2010), 389–410.
 33. P. H. Leslie and J. C. Gower, The properties of a stochastic model for the predatorprey type of interaction between two species, Biometrika, 47 (1960), 219–234.
 34. H. Liu and H. Cheng, Dynamic analysis of a preypredator model with statedependent control strategy and square root response function, Adv. Differ. Equ., 2018 (2018), 63.
 35. J. Wang, H. Cheng, H. Liu, et al., Periodic solution and control optimization of a preypredator model with two types of harvesting, Adv. Differ. Equ., 2018 (2018), 41.
 36. T. Liu and H. Dong, The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its InitialBoundary Value Problem on the Half Line via the RiemannHilbert Approach Mathematics, 7 (2019), 170.
 37. Q. Wang, Y. Zhang, Z. Wang, et al., Periodicity and attractivity of a ratiodependent Leslie system with impulses, J. Math. Anal. Appl., 376 (2011), 212–220.
 38. S. Tang, B. Tang, A. Wang,et al., Holling Ⅱ predatorprey impulsive semidynamic model with complex Poincaré map, Nonlinear Dyn., 81 (2015), 1575–1596.
 39. T. Zhang, X. Liu, X. Meng, et al., Spatiotemporal dynamics near the steady state of a planktonic system, Comput. Math. Appl., 75 (2018), 4490–4504.
 40. M. Han, L. Zhang, Y. Wang, et al., The effects of the singular lines on the traveling wave solutions of modified dispersive water wave equations, Nonlinear AnalReal., 47 (2019), 236–250.
 41. F. Liu, Z. Fu and S. T. Jhang, Boundedness and continuity of marcinkiewicz integrals associated to homogeneous mappings on TriebelLizorkin spaces, Front. Math. China, 14 (2019), 95–122.
 42. F. Liu, Rough maximal functions supported by subvarieties on TriebelLizorkin spaces Revista de la Real Academia de Ciencias Exactas, F´ ısicas y Naturales. Serie A. Matemáticas, 112 (2018), 593–614.
 43. X. Meng, F. Li and S. Gao, Global analysis and numerical simulations of a novel stochastic ecoepidemiological model with time delay, Appl. Math. Comput., 339 (2018), 701–726.
 44. R. P. Gupta and M. Banerjee, Bifurcation analysis and control of LeslieGower predatorprey model with MichaelisMenten type preyharvesting, Differ. Equ. Dyn. Syst., 20 (2012), 339–366.
 45. Z. Zhao, L. Yang and L. Chen, Impulsive perturbations of a predatorprey system with modified LeslieGower and Holling type Ⅱ schemes J. Appl. Math. Comput., 35 (2011), 119–134.
 46. C. Wei and L. Chen, A LeslieGower pest manangement model with impulsive state feedback control, J. Biomath., 27 (2012), 621–628.
 47. J. D. Flores and E. GonzálezOlivares, A modified LeslieGower predatorprey model with ratiodependent functional response and alternative food for the predator, Math. Methods Appl. Sci., 40 (2017), 23132328.
 48. Z. Liang and H. Pan, Qualitative analysis of a ratiodependent HollingTanner model, Math. Anal. Appl., 334 (2007), 954–964.
 49. K. Sun, T. Zhang and Y. Tian, Theoretical study and control optimization of an integrated pest management predatorprey model with power growth rate, Math. Biosci., 279 (2012), 13–26.
 50. C. Wei, J. Liu and L. Chen, Homoclinic bifurcation of a ratiodependent predatorprey system with impulsive harvesting, Nonlinear Dyn., (2017), 1–12.
 51. Z. Liang, X. Zeng, G. Pang, et al., Periodic solution of a Leslie predatorprey system with ratiodependent and state impulsive feedback control Nonlinear Dyn., (2017), 1–15.
 52. Y. Tian, K. Sun and L. Chen, Geometric approach to the stability analysis of the periodic solution in a semicontinuous dynamic system, Int. J. Biomath., 7 (2014), 1450018.
 53. C. J. Edholm, B. Tenhumberg, C. Guiver, et al., Management of invasive insect species using optimal control theory, Ecol. Model., 381 (2018), 36–45.
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