633
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Dynamic analysis of stochastic delay mutualistic system of leaf-cutter ants with stage structure and their fungus garden

, &
Pages 565-584 | Received 22 Jun 2021, Accepted 17 Mar 2022, Published online: 18 Jul 2022

References

  • W.G. Aiello and H.I. Freedman, A time-delay model of single-species growth with stage structure, Math. Biosci. 101 (1990), pp. 139–153.
  • J.F.M. Al-Omari, A stage-structured predator-prey model with distributed maturation delay and harvesting, J. Biol. Dyn. 9 (2015), pp. 278–287.
  • J.R. Beddington, Mutural interference between parasites or predators and its effect on searching efficiency, J. Animal Ecology 44 (1975), pp. 331–340.
  • Y.M. Cai, S.Y. Cai, and X.R. Mao, Stochastic delay foraging arena predator–prey system with Markov switching, Stoch. Anal. Appl. 38 (2020), pp. 191–212.
  • Z.W. Chen, R.M. Zhang, J. Li, S.W. Zhang, and C.J. Wei, A stochastic nutrient-phytoplankton model with viral infection and Markov switching, Chaos Solitons Fractals 140 (2020), p. 110109.
  • D.L. DeAngelis, R.A. Goldstein, and R. O'neill, A model for trophic interacting, Ecology 56 (1975), pp. 811–892.
  • Y. Deng and M. Liu, Analysis of a stochastic tumor-immune model with regime switching and impulsive perturbations, Appl. Math. Model. 78 (2020), pp. 482–504.
  • C.H. Feng, Existence and uniqueness of positive almost periodic solutions for a class of impulsive Lotka–Volterra cooperation models with delays, British J. Math. Computer Sci. 22 (2017), pp. 1–8.
  • D. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev. 43 (2001), pp. 525–545.
  • Y.L. Huang, W.Y. Shi, C.J. Wei, and S.W. Zhang, A stochastic predator–prey model with Holling II increasing function in the predator, J. Biol. Dyn. 15 (2021), pp. 1–18.
  • W. Ji and M. Liu, Optimal harvesting of a stochastic commensalism model with time delay, Phys. A Statist. Mechan. Appl. 527 (2019), p. 121284.
  • Y. Kang, R. Clark, M. Makiyama, and J. Fewell, Mathematical modeling on obligate mutualism: interactions between leaf-cutter ants and their fungus garden, J. Theor. Biol. 289 (2011), pp. 116–127.
  • Q. Liu, D. Jiang, T. Hayat, A. Alsaedi, and B. Ahmad, Dynamical behavior of a stochastic predator-prey model with stage structure for prey, Stoch. Anal. Appl. 38 (2020), pp. 647–667.
  • G.D. Liu, H.K. Qi, Z.B. Chang, and X.Z. Meng, Asymptotic stability of a stochastic may mutualism system, Comput. Math. Appl. 79 (2020), pp. 735–745.
  • C. Liu, Q. Zhang, Y. Zhang, and X. Duan, Bifurcation and control in a differential-algebraic harvested prey–predator model with stage structure for predator, Int. J. Bifurcation Chaos 18 (2008), pp. 3159–3168.
  • A.J. Lotka, Elements of physical biology, Am. J. Public. Health.15 (1925), p. 812.
  • X.R. Mao, Stochastic Differential Equations and Applications, Horwood Publishing, West Sussex, 1997.
  • M. Peng and D.Z. Zhang, Bifurcation analysis and control of a delayed stage-structured predator–prey model with ratio-dependent Holling type III functional response, J. Vibration Control 26 (2020), pp. 1232–1245.
  • Y. Takeuchi, Y. Saito, and S. Nakaoka, Stability, delay, and chaotic behavior in a Lotka–Volterra predator–prey system, Math. Biosci. Eng. 3 (2006), pp. 173–187.
  • V. Volterra, Variations and fluctuations of the number of individuals in animal species living together, ICES J. Marine Sci. 3 (1928), pp. 3–51.
  • W.D. Wang and L.S. Chen, A predator–prey system with stage-structure for predator, Computers Math. Appl. 33 (1997), pp. 83–91.
  • J. Wei, Bifurcation analysis in a scalar delay differential equation, Nonlinearity 20 (2007), pp. 2483–2498.
  • F.Y. Wei and Q.Y. Fu, Globally asymptotic stability of a predator-prey model with stage structure incorporating prey refuge, Int. J. Biomath. 9 (2016), p. 1650058.
  • X.J. Yao and F.J. Qin, On four positive almost periodic solutions to a Lotka–Volterra cooperative system with impulses and harvesting terms, J. Southwest China Normal University 4 (2016), pp. 7–14.
  • X.W. Yu and S.L. Yuan, Asymptotic properties of a stochastic chemostat model with two distributed delays and nonlinear perturbation, Discrete Continuous Dyn. Systems Ser B 25 (2020), pp. 2373–2390.