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Exploring the Impact of Distributed Delay and Environmental Fluctuation on Food Chain Stability in a Chemostat Model

  • Miaomiao Gao [1] ; Xiao Chen [1] ; Daqing Jiang [2]
    1. [1] Qingdao University

      Qingdao University

      China

    2. [2] China University of Petroleum (East China)
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • The food chain chemostat model is a mathematical model employed to evaluate the stability of food chains and the responsiveness of ecosystems. Based on the relationships and interactions among various species within the food chain, the model discloses changes in population size and the adaptability of ecosystems to environmental changes by analyzing the flow of energy and matter. In this study, we propose the predator-prey chemostat model incorporating log-normal Ornstein-Uhlenbeck process and distributed delay, and study dynamics of the stochastic system. Initially, we establish existence and uniqueness of the global positive solution. Next, threshold conditions for the extinction in two scenarios are derived: one where both predator and prey become extinct, and another where predator goes extinct while the prey survives.

      Additionally, the stationary distribution indicates the long-term coexistence of prey and predator. By constructing suitable Lyapunov functions, we get the sufficient condition for existence of the stationary distribution. Then the explicit form of the density function near the positive equilibrium of the corresponding deterministic system is provided. Finally, we use numerical simulations to study the influence of mean delay, volatility intensity, and reversion speed on biological population.

  • Referencias bibliográficas
    • 1. Tovey, M.G.: The cultivation of animal cells in the chemostat: application to the study of tumor cell multiplication. Adv. Cancer Res....
    • 2. Ali, E., Asif, M., Ajbar, A.: Study of chaotic behavior in predator-prey interactions in a chemostat. Ecol. Model. 259, 10–15 (2013)
    • 3. Wolkowicz, G.S.K., Xia, H., Ruan, S.: Competition in the chemostat: A distributed delay model and its global asymptotic behavior. SIAM...
    • 4. Sun, M., Dong, Q., Wu, J.: Asymptotic behavior of a Lotka-Volterra food chain stochastic model in the chemostat. Stoch. Anal. Appl. 35(4),...
    • 5. Gao, M., Jiang, D., Hayat, T., Alsaedi, A.: Threshold behavior of a stochastic Lotka-Volterra food chain chemostat model with jumps. Physica...
    • 6. Droop, M.R.: Vitamin B12 and marine ecology . IV. The kinetics of uptake, growth and inhibition in Monochrysis lutheri. J. Mar. Biol. Assoc....
    • 7. Scudo, F.M., Ziegler, J.R.: The Golden Age of Theoretical Ecology: 1923–1940. Springer Science & Business Media, New York (2013)
    • 8. Cushing, J.M.: Integrodifferential Equations and Delay Models in Population Dynamics. Springer Science & Business Media, New York (2013)
    • 9. MacDonald, N.: Time Lags in Biological Models. Springer Science & Business Media, New York (2013)
    • 10. Liu, M., Bai, C.: Analysis of a stochastic tri-trophic food-chain model with harvesting. J. Math. Biol. 73, 597–625 (2016)
    • 11. Hening, A., Nguyen, D.H.: Stochastic Lotka-Volterra food chains. J. Math. Biol. 77, 135–163 (2018)
    • 12. Tuerxun, N., Teng, Z., Muhammadhaji, A.: Global dynamics in a stochastic three species food-chain model with harvesting and distributed...
    • 13. Yang, A., Yuan, S., Zhang, T.: Environmental stochasticity driving the extinction of top predators in a food chain chemostat model. J....
    • 14. Liu, R., Ma, W.: Noise-induced stochastic transition: A stochastic chemostat model with two complementary nutrients and flocculation effect....
    • 15. Fatehi Nia, M., Khajoei, N.: Stability and bifurcation of stochastic chemostat model. J. Math. Model. 11(2), 375–394 (2023)
    • 16. Sun, S., Sun, Y., Zhang, G., Liu, X.: Dynamical behavior of a stochastic two-species Monod competition chemostat model. Appl. Math. Comput....
    • 17. Xu, C., Yuan, S.: An analogue of break-even concentration in a simple stochastic chemostat model. Appl. Math. Lett. 48, 62–68 (2015)
    • 18. Zhao, D., Yuan, S.: Sharp conditions for the existence of a stationary distribution in one classical stochastic chemostat. Appl. Math....
    • 19. Zhang, S., Yuan, S., Zhang, T.: A predator-prey model with different response functions to juvenile and adult prey in deterministic and...
    • 20. Laaribi, A., Boukanjime, B., El Khalifi, M., Bouggar, D., El Fatini, M.: A generalized stochastic SIRS epidemic model incorporating mean-reverting...
    • 21. Wang, W., Cai, Y., Ding, Z., Gui, Z.: A stochastic differential equation SIS epidemic model incorporating Ornstein-Uhlenbeck process....
    • 22. Ayoubi, T., Bao, H.: Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process. Appl....
    • 23. López-de-la Cruz, J.: Random and stochastic disturbances on the input flow in chemostat models with wall growth. Stoch. Anal. Appl. 37(4),...
    • 24. Hu, R., Han, C., Wu, Y., Ai, X.: Analysis of a stochastic Leslie-Gower three-species food chain system with Holling-II functional response...
    • 25. Zhang, X.: A stochastic non-autonomous chemostat model with mean-reverting Ornstein-Uhlenbeck process on the washout rate. J. Dyn. Differ....
    • 26. Trost, D.C., Overman, E., Ostroff, J.H., Xiong, W., March, P.: A model for liver homeostasis using modified mean-reverting Ornstein-Uhlenbeck...
    • 27. Xu, X., Tian, B., Chen, X., Qiu, Y.: Dynamics of a stochastic food chain chemostat model with MonodHaldane functional response and Ornstein-Uhlenbeck...
    • 28. Allen, E.: Environmental variability and mean-reverting processes. Discrete Contin. Dyn. Syst. Ser. B. 21(7), 2073–2089 (2016)
    • 29. Gao,M., Jiang, D., Ding, J.: Dynamical behavior of a nutrient-plankton model with Ornstein-Uhlenbeck process and nutrient recycling. Chaos...
    • 30. Shi, Z., Jiang, D.: Dynamics and density function of a stochastic COVID-19 epidemic model with Ornstein-Uhlenbeck process. Nonlinear Dyn....
    • 31. Peng, S., Zhu, X.: Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations. Stochastic...
    • 32. Meyn, S.P., Tweedie, R.L.: Stability of Markovian processes III: Foster-Lyapunov criteria for continuous-time processes. Adv. Appl. Probab....
    • 33. Du, N.H., Nguyen, D.H., Yin, G.G.: Conditions for permanence and ergodicity of certain stochastic predator-prey models. J. Appl. Probab....
    • 34. Ma, Z., Zhou, Y., Li, C.: Qualitative and Stability Methods for Ordinary Differential Equations. Science Press, Beijing (2015)
    • 35. Oksendal, B.: Stochastic Differential Equations: An Introduction with Applications. Springer-Verlag, Heidelberg, New York (2000)
    • 36. Mao, X.: Stochastic Differential Equations and Applications. Horwood Publishing, Chichester (1997)
    • 37. Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43(3), 525–546 (2001)
    • 38. Zhang, X., Yuan, R.: Stochastic properties of solution for a chemostat model with a distributed delay and random disturbance. Int. J....
    • 39. Caswell, H., Neubert, M.G.: Chaos and closure terms in plankton food chain models. J. Plankton Res. 20(9), 1837–1845 (1998)
    • 40. Abrams, P.A., Quince, C.: The impact of mortality on predator population size and stability in systems with stage-structured prey. Theor....
    • 41. Mukhopadhyay, B., Bhattacharyya, R.: A stage-structured food chain model with stage dependent predation: Existence of codimension one...
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