Dynamical Behavior of a Stochastic Microorganism Flocculation Model with Nonlinear Perturbation

• Xiaojie Mu ^[2] ; Daqing Jiang ^[2] ; Ahmed Alsaedi ^[1]
  1. [1] King Abdulaziz University

     King Abdulaziz University

     Arabia Saudí

     
  2. [2] China University of Petroleum (East China)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Due to many uncertain factors, the microorganism flocculation models could be affected by environmental noise. The paper aims to discuss the dynamical behavior of a stochastic microorganism flocculation model, including the extinction and the persistence. Moreover, the expression of density function near the positive equilibrium point is explicitly obtained. Our results indicate that a larger white noise can accelerate the extinction of microorganism, while a weaker white noise can guarantee the existence of stationary distribution. In addition, our theory is confirmed by some numerical examples.

• Referencias bibliográficas
  • 1. Tai, X., Ma, W., Guo, S., et al.: A class of dynamic delayed model describing flocculation of micoorganism and its theoretical analysis....
  • 2. Guo, S., Ma, W.: Global dynamics of a microorganism flocculation model with time delay. Commun. Pure Appl. Anal. 16(5), 1883–1891 (2017)
  • 3. Guo, S., Ma, W., Zhao, X.: Global dynamics of a time-delayed microorganism flocculation model with saturated functional responses. J. Dyn....
  • 4. Aldajani, M., Alipoormazandarani, N., Kong, F., et al.: Acid hydrolysis of kraft lignin-acrylamide polymer to improve its flocculation...
  • 5. Zhang, T., Ma, W., Meng, X.: Dynamical analysis of a continuous-culture and harvest chemostat model with impulsive effect. J. Biol. Syst....
  • 6. Zhang, H., Zhang, T.: Asymptotic behavior of a stochastic microorganism flocculation model with time delay. Appl. Math. Lett. 121(1), 107384...
  • 7. Guo, S., Cui, J., Ma, W.: An analysis approach to permanence of a delay differential equations model of microorganism flocculation. Discrete...
  • 8. Zhao, Z., Zhang, X., Chen, L.: Nonlinear modelling of chemostat model with time delay and impulsive effect. Nonlinear Dyn. 63(1), 95–104...
  • 9. Zhang, H., Zhang, T.: The stationary distribution of a microorganism flocculation model with stochastic perturbation. Appl. Math. Lett....
  • 10. Liu, Q., Jiang, D., Hayat, T., et al.: Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order...
  • 11. Liu, Q., Jiang, D.: Stationary distribution and extinction of a stochastic SIR model with nonlinear perturbation. Appl. Math. Lett. 73,...
  • 12. Han, B., Jiang, D., Hayat, T., et al.: Stationary distribution and extinction of a stochastic staged progression AIDS model with staged...
  • 13. Ikeda, N., Watanabe, S.: A comparison theorem for solutions of stochastic differential equations and applications. J. Math. 14, 619–633...
  • 14. Zhou, B., Jiang, D., Dai, Y., et al.: Stationary distribution and probability density function of a stochastic SVIS epidemic model with...
  • 15. Mao, X.: Stochastic Differential Equations and Applications. Horwood Publishing, second edition, (1997)
  • 16. Bao, K., Rong, L., Zhang, Q.: Analysis of a stochastic SIRS model with interval parameters. Discrete Contin. Dyn. Syst. Ser. B 24(9),...
  • 17. Sadovsky, M., Senashova, M.: Model of prey-predator dynamics with reflexive spatial behaviour of species based on optimal migration. Bull....
  • 18. Has’miniskii, R.: Stochastic Stability of Differential Equations. Sijthoff & Noordhoff, (1980)
  • 19. Rudnicki, R.: Asymptotic properties of the Fokker-Planck equation, pp. 517–521. Springer, Berlin, Heidelberg (1995) Springer, Berlin Heidelberg...
  • 20. Higham, D.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 433, 525–546 (2001)