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Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator

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  • Saifuddin, Md.
  • Biswas, Santanu
  • Samanta, Sudip
  • Sarkar, Susmita
  • Chattopadhyay, Joydev

Abstract

The paper explores an eco-epidemiological model with weak Allee in predator, and the disease in the prey population. We consider a predator-prey model with type II functional response. The curiosity of this paper is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We perform the local and global stability analysis of the equilibrium points and the Hopf bifurcation analysis around the endemic equilibrium point. Further we pay attention to the chaotic dynamics which is produced by disease. Our numerical simulations reveal that the three species eco-epidemiological system without weak-Allee induced chaos from stable focus for increasing the force of infection, whereas in the presence of the weak-Allee effect, it exhibits stable solution. We conclude that chaotic dynamics can be controlled by the Allee parameter as well as the competition coefficients. We apply basic tools of non-linear dynamics such as Poincare section and maximum Lyapunov exponent to identify chaotic behavior of the system.

Suggested Citation

  • Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:270-285
    DOI: 10.1016/j.chaos.2016.06.009
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    References listed on IDEAS

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    1. John M. Drake, 2004. "Allee Effects and the Risk of Biological Invasion," Risk Analysis, John Wiley & Sons, vol. 24(4), pages 795-802, August.
    2. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    3. Zhang, Tongqian & Ma, Wanbiao & Meng, Xinzhu & Zhang, Tonghua, 2015. "Periodic solution of a prey–predator model with nonlinear state feedback control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 95-107.
    4. Peng, Yahong & Zhang, Tonghua, 2016. "Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 1-12.
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    Cited by:

    1. Alzahrani, Abdullah K. & Alshomrani, Ali Saleh & Pal, Nikhil & Samanta, Sudip, 2018. "Study of an eco-epidemiological model with Z-type control," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 197-208.
    2. Biswas, Santanu, 2017. "Mathematical modeling of Visceral Leishmaniasis and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 546-556.
    3. Bashkirtseva, Irina & Perevalova, Tatyana & Ryashko, Lev, 2020. "Noise-induced shifts in dynamics of multi-rhythmic population SIP-model," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Yang, Yafei & Fan, Meng, 2023. "Impact of selective grazing on the dynamics of a diffusive plankton model with component Allee effect and additional food," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    5. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2020. "Analysis of regular and chaotic dynamics in a stochastic eco-epidemiological model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Fu, Shuaiming & Luo, Jianfeng & Zhao, Yi, 2022. "Stability and bifurcations analysis in an ecoepidemic system with prey group defense and two infectious routes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 665-690.
    7. Sarangi, B.P. & Raw, S.N., 2023. "Dynamics of a spatially explicit eco-epidemic model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 241-263.

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