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Research Article

Hopf bifurcation in delayed nutrient-microorganism model with network structure

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Pages 1-13 | Received 26 Apr 2021, Accepted 23 Nov 2021, Published online: 10 Jan 2022

References

  • M. Baurmann and U. Feudel, Turing patterns in a simple model of a nutrient-microorganism system in the sediment, Ecol. Complex. 1 (2004), pp. 77–94.
  • M. Bentounsi, I. Agmour, and N. Achtaich, The Hopf bifurcation and stability of delayed predator-prey system, Comput. Appl. Math. 37(5) (2018), pp. 5702–5714.
  • M.X. Chen, R.C. Wu, B. Liu, and L.P. Chen, Hopf-Hopf bifurcation in the delayed nutrient-microorganism model, Appl. Math. Model. 86 (2020), pp. 460–483.
  • Y. Ide, H. Izuhara, and T. Machidac, Turing instability in reaction diffusion models on complex networks, Physica A. 457 (2016), pp. 331–347.
  • A. Kumar and B. Dubey, Modeling the effect of fear in a prey-predator system with prey refuge and gestation delay, Int. J. Bifurcat. Chaos. 29(14) (2019), pp. 1950195.
  • Y.Q. Liu, D.F. Duan, and B. Niu, Spatiotemporal dynamics in a diffusive predator prey model with group defense and nonlocal competition, Appl. Math. Lett. 103 (2020), pp. 106175.
  • K. Manna and M. Banerjee, Stability of Hopf-bifurcating limit cycles in a diffusion-driven prey-predator system with Allee effect and time delay, Math. Biosci. Eng. 16(4) (2019), pp. 2411–2446.
  • B. Roy, S.K. Roy, and D.B. Gurung, Holling-Tanner model with Beddington-DeAngelis functional response and time delay introducing harvesting, Math. Comput. Simul. 142 (2017), pp. 1–14.
  • Y.L. Shi, Z.H. Liu, and C.R. Tian, Hopf bifurcation in an activator-inhibitor system with network, Appl. Math. Lett. 98 (2019), pp. 22–28.
  • C.R. Tian, Z. Ling, and L. Zhang, Delay-driven spatial patterns in a network-organized semiarid vegetation model, Appl. Math. Comput. 367 (2020), pp. 124778.
  • T.H. Zhang, Y.L. Song, and H. Zang, The stability and Hopf bifurcation analysis of a gene expression model, J. Math. Anal. Appl. 395 (2012), pp. 103–113.
  • H.Y. Zhao and D.Y. Wu, Point to point traveling wave and periodic traveling wave induced by Hopf bifurcation for a diffusive predator-prey system, Discrete Cont. Dyn. Syst. S. 13(11) (2020), pp. 3271–3284.