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Journal of Biological Dynamics Volume 16, 2022 - Issue 1
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Tianyuan Hengyang Workshop 2020

The state-dependent impulsive control for a general predator–prey model

Xiaoxiao ZhuSchool of Mathematics and Physics, University of South China, Hengyang, People's Republic of ChinaCorrespondence[email protected]
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,
Huilan WangSchool of Mathematics and Physics, University of South China, Hengyang, People's Republic of ChinaCorrespondence[email protected]
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Zigen OuyangSchool of Mathematics and Physics, University of South China, Hengyang, People's Republic of ChinaCorrespondence[email protected]
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Pages 354-372 | Received 04 Feb 2021, Accepted 22 May 2021, Published online: 05 Jun 2021

References

  • D. Bainov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific & Technical, England, 1993.
  • E. Borducchi, C. Cabral, K. Stephenson, J. Liu, and H. Dan, Ad26/mva therapeutic vaccination with tlr7 stimulation in siv-infected rhesus monkeys, Nature 540 (2016), pp. 284–287.
  • J. Chavez, D. Jungmann, and S. Siegmund, A comparative study of integrated pest management strategies based on impulsive control, J. Biological Dyn. 12 (2018), pp. 318–341.
  • T. Cheng, S. Tang, and R.A. Cheke, Threshold dynamics and bifurcation of a state-dependent feedback nonlinear control SIR model, J. Comput. Nonlinear Dyn. 14 (2019), pp. 209.
  • R. Hakl, M. Pinto, and V. Tkachenko, Almost periodic evolution systems with impulse action at state-dependent moments, J. Math. Anal. Appl. 446 (2017), pp. 1030–1045.
  • Z. He, C. Li, L. Chen, and Zh. Cao, Dynamic behaviors of the FitzHugh–Nagumo neuron model with state-dependent impulsive effects, Neural Netw. 121 (2019), pp. 497–511. 
  • X. Hu, J. Li, and X. Feng, Threshold dynamics of a HCV model with virus to cell transmission in both liver with CTL immune response and the extrahepatic tissue, J. Biological Dyn. 15 (2021), pp. 19–34.
  • G. Jiang, Q. Lu, and L. Qian, Complex dynamics of a Holling type II prey–predator system with state feedback control, Chaos Solit. Fract. 31 (2007), pp. 448–461.
  • T. Kar and S. Chattopadhyay, A focus on long-run sustainability of a harvested prey predator system in the presence of alternative prey, Comp. Rend. Biol. 333 (2010), pp. 841–849.
  • L. Li, Ch. Li, and W. Zhang, Existence of solution, pulse phenomena and stability criteria for state-dependent impulsive differential equations with saturation, Commun. Nonlinear Sci. Numer. Simul. 77 (2019), pp. 312–323.
  • M. Liao, Y. Liu, Sh. Liu, and A. Meyad, Stability and Hopf bifurcation of HIV-1 model with Holling II infection rate and immune delay, J. Biological Dyn. (2021). Available at DOI:https://doi.org/10.1080/17513758.2021.1895334.
  • L. Nie, J. Shen, and C. Yang, Dynamic behavior analysis of SIVS epidemic models with state-dependent pulse vaccination, Nonlinear Anal. Hybrid Syst. 27 (2018), pp. 258–270.
  • L. Nie, Zh. Teng, H. Lin, and J. Peng, The dynamics of a Lotka-Volterra predator-prey model with state dependent impulsive harvest for predator, BioSystems 98 (2009), pp. 67–72.
  • M. Nowak and R. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000.
  • P. Simeonov and D. Bainov, Orbital stability of periodic solutions of autonomous systems with impulse effect, Int. J. Syst. Sci.19 (1989), pp. 2561–2585.
  • S. Tang and R. Cheke, State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences, Math. Biol. 50 (2005), pp. 257–292.
  • X. Tang and X. Fu, On period-k solution for a population system with state-dependent impulsive effect, J. Appl. Anal. Comput. 7 (2017), pp. 39–56.
  • S. Tang, X. Tan, and J. Yang, Periodic solution bifurcation and spiking dynamics of impacting predator–prey dynamical model, Int. J. Bifurcation Chaos 28 (2018), pp. 1850147. Article ID 1850147.
  • J. Wang, H. Chen, Y. Li, and X. Zhang, The geometrical analysis of a predator-prey model with multi-state dependent impulses, J. Appl. Anal. Comput. 8 (2018), pp. 427–442.
  • H. Wang, B. Dai, and Q. Xiao, Existence of order-1 periodic solutions for a viral infection model with state-dependent impulsive control, Adv. Differ. Eq. 2019 (1) (2019). Available at https://doi.org/10.1186/s13662-019-1967-x.
  • H. Wang, Ch. Ou, and B. Dai, The existence and stability of order-1 periodic solutions for an impulsive Kolmogorov predator–prey model with non-selective harvesting, J. Appl. Anal. Comput. 11(2021), pp. 1348–1370.
  • A. Wang, Y. Xiao, and R. Smith, Using non-smooth models to determine thresholds for microbial pest management, J. Math. Biol. 78 (2019), pp. 1389–1424.
  • Ch. Xu, M. Liao, P. Li, Y. Guo, Q. Xiao, and Sh. Yuan, Influence of multiple time delays on bifurcation of fractional-order neural networks, Appl. Math. Comput. 361 (2019), pp. 565–582.
  • G. Zeng, L. Chen, and L. Sun, Existence of periodic solution of order one of planar impulsive autonomous system, J. Comput. Appl. Math. 186 (2006), pp. 466–481.
  • Q. Zhang, B. Tang, and S. Tang, Vaccination threshold size and backward bifurcation of SIR model with state-dependent pulse control, J. Theoretical Biol. 455 (2018), pp. 75–85.
  • Y. Zhou, Ch. Li, and H. Wang, Stability analysis on state-dependent impulsive hopfield neural networks via fixed-time impulsive comparison system method, Neurocomputing 316 (2018), pp. 20–29.

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