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Fold-flip and strong resonance bifurcations of a discrete-time mosquito model

Author

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  • Chen, Qiaoling
  • Teng, Zhidong
  • Wang, Feng

Abstract

In this paper we consider a two-dimensional discrete-time mosquito model, in which sterile mosquitoes are released into the wild at a nonlinear saturated rate. By reducing the discrete model into different normal forms, we prove that there exists a series of bifurcations of codimension two, including fold-flip bifurcation and strong resonance bifurcations (1:1, 1:2), when the values of two parameters vary. To verify theoretical analyses and confirm the chaotic behaviors of the discrete-time mosquito model, the bifurcation diagrams, phase portraits, time-series diagrams and maximum Lyapunov exponents diagrams are also showed for some special cases.

Suggested Citation

  • Chen, Qiaoling & Teng, Zhidong & Wang, Feng, 2021. "Fold-flip and strong resonance bifurcations of a discrete-time mosquito model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000576
    DOI: 10.1016/j.chaos.2021.110704
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    References listed on IDEAS

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    1. Qiaoling Chen & Zhidong Teng & Junli Liu & Feng Wang, 2020. "Codimension-2 Bifurcation Analysis and Control of a Discrete Mosquito Model with a Proportional Release Rate of Sterile Mosquitoes," Complexity, Hindawi, vol. 2020, pages 1-18, August.
    2. Hu, Zengyun & Teng, Zhidong & Zhang, Tailei & Zhou, Qiming & Chen, Xi, 2017. "Globally asymptotically stable analysis in a discrete time eco-epidemiological system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 20-31.
    3. Cui, Qianqian & Zhang, Qiang & Qiu, Zhipeng & Hu, Zengyun, 2016. "Complex dynamics of a discrete-time predator-prey system with Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 158-171.
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