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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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    1. Owolabi, Kolade M. & Pindza, Edson, 2019. "Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 146-157.
    2. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    3. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Banerjee, Ritwick & Das, Pritha & Mukherjee, Debasis, 2018. "Stability and permanence of a discrete-time two-prey one-predator system with Holling Type-III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 240-248.
    5. Elettreby, M.F., 2009. "Two-prey one-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2018-2027.
    6. Atangana, Abdon & Shafiq, Anum, 2019. "Differential and integral operators with constant fractional order and variable fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 226-243.
    7. Mbava, W. & Mugisha, J.Y.T. & Gonsalves, J.W., 2017. "Prey, predator and super-predator model with disease in the super-predator," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 92-114.
    8. Zeng, Ting & Teng, Zhidong & Li, Zhiming & Hu, Junna, 2018. "Stability in the mean of a stochastic three species food chain model with general Le´vy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 258-265.
    9. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    10. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    11. Fathalla A. Rihan & Dumitru Baleanu & S. Lakshmanan & R. Rakkiyappan, 2014. "On Fractional SIRC Model with Salmonella Bacterial Infection," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, April.
    12. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    13. Fathalla A. Rihan, 2013. "Numerical Modeling of Fractional-Order Biological Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, August.
    14. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
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    Cited by:

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    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    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).

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