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Complex dynamics of a four-species food web model with nonlinear top predator harvesting and fear effect

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  • Shang, Zuchong
  • Qiao, Yuanhua

Abstract

In this paper, a four-species food web model is formulated to investigate the influence of fear effect and nonlinear top predator harvesting on the dynamical behaviors. The global stability of the system at the interior equilibrium is explored by Li–Muldowney geometric approach. By applying the Sotomayor’s theorem, it is shown that the system undergoes transcritical bifurcation and pitchfork bifurcation. The conditions for the occurrence of Hopf bifurcation are established, and the stability of the bifurcating limit cycle is discussed by normal form theory. Finally, the numerical simulations are carried out. It is observed that the system presents chaotic dynamics, periodic window and chaotic attractors. Two distinct routes to chaos are discovered, one is period doubling cascade and the other is the generation and destruction of quasi-periodic states. Moreover, it is found that the fear effect can suppress fluctuations in population density to stabilize the system.

Suggested Citation

  • Shang, Zuchong & Qiao, Yuanhua, 2024. "Complex dynamics of a four-species food web model with nonlinear top predator harvesting and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 458-484.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:458-484
    DOI: 10.1016/j.matcom.2024.04.024
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    References listed on IDEAS

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    1. Fangyuan Hua & Kathryn E. Sieving & Robert J. Fletcher & Chloe A. Wright, 2014. "Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(3), pages 509-519.
    2. Lutz Becks & Frank M. Hilker & Horst Malchow & Klaus Jürgens & Hartmut Arndt, 2005. "Experimental demonstration of chaos in a microbial food web," Nature, Nature, vol. 435(7046), pages 1226-1229, June.
    3. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    4. Elisa Benincà & Jef Huisman & Reinhard Heerkloss & Klaus D. Jöhnk & Pedro Branco & Egbert H. Van Nes & Marten Scheffer & Stephen P. Ellner, 2008. "Chaos in a long-term experiment with a plankton community," Nature, Nature, vol. 451(7180), pages 822-825, February.
    5. Wang, Fengyan & Pang, Guoping, 2008. "Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1366-1376.
    6. Sk, Nazmul & Tiwari, Pankaj Kumar & Pal, Samares, 2022. "A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 136-166.
    7. Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.
    8. Thirthar, Ashraf Adnan & Majeed, Salam J. & Alqudah, Manar A. & Panja, Prabir & Abdeljawad, Thabet, 2022. "Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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