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Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators

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  • Rihan, F.A.
  • Rajivganthi, C

Abstract

In this work, we study the dynamics of a fractional-order delay differential model of prey-predator system with Holling-type III and predator population is infected by an infectious disease. We use Laplace transform, Lyapunov functional, and stability criterion to establish new sufficient conditions that ensure the asymptotic stability of the steady states of the system. Existence of Hopf bifurcation is investigated. The model undergoes Hopf bifurcation, when the feedback time-delays passes through the critical values τ1* and τ2*. Fractional-order improves the dynamics of the model; while time-delays play a considerable influence on the creation of Hopf bifurcation and stability of the system. Some numerical simulations are provided to validate the theoretical results.

Suggested Citation

  • Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307608
    DOI: 10.1016/j.chaos.2020.110365
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    Cited by:

    1. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    2. Zou, Xiaoling & Li, Qingwei & Cao, Wenhao & Lv, Jingliang, 2023. "Thresholds and critical states for a stochastic predator–prey model with mixed functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 780-795.
    3. Chen, Xingzhi & Tian, Baodan & Xu, Xin & Zhang, Hailan & Li, Dong, 2023. "A stochastic predator–prey system with modified LG-Holling type II functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 449-485.
    4. Alsakaji, Hebatallah J. & Kundu, Soumen & Rihan, Fathalla A., 2021. "Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    5. Elsayed I. Mahmoud & Temirkhan S. Aleroev, 2022. "Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation," Mathematics, MDPI, vol. 10(17), pages 1-12, September.
    6. Srinivas, M.N. & Sreerag, C. & Madhusudanan, V. & Gul, Nadia & Khan, Zareen A. & Zeb, Anwar, 2022. "Spatial deployment and performance of diffusion coefficients of two preys and one predator ecological system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    7. He, Ke & Shi, Jianping & Fang, Hui, 2024. "Bifurcation and chaos analysis of a fractional-order delay financial risk system using dynamic system approach and persistent homology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 253-274.
    8. Li, Ning & Yan, Mengting, 2022. "Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    9. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.

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