Skip to main content
SpringerLink
Log in

Dynamical analysis in a stochastic bioeconomic model with stage-structuring

  • Original Article
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This article studies a class of stage-structured bioeconomic models with stochastic fluctuations. The stochastic bioeconomic model is simplified to Itô equation by stochastic averaging method. The stochastic stability, Hopf bifurcation, D-bifurcation and P-bifurcation are discussed based on the system’s maximal Lyapunov exponent and dynamic systems invariant measure Lyapunov exponent. Numerical simulations are presented to illustrate our main results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Zhang, Y., Zhang, Q.L.: Dynamic behavior in a delayed stage-structured population model with stochastic fluctuation and harvesting. Nonlinear Dyn. 66, 231–245 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhang, X.A., Chen, L.S., Neumann, A.U.: The stage structured predator–prey model and optimal harvesting policy. Math. Biosci. 168, 201–210 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Sun, C.J., Lin, Y.P., Han, M.A.: Dynamic analysis for a stage-structure competitive system with mature population harvesting. Chaos Solitons Fractals 31, 380–390 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang, J., Wang, K.: The optimal harvesting problems of a stage-structured population. Appl. Math. Comput. 148, 235–247 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Nisbet, R.M., Gurney, W.S.C.: Modelling Fluctuating Populations. Wiley Interscience, New York (1982)

    MATH  Google Scholar 

  6. Saha, T., Bandyopadhyay, M.: Dynamical analysis of a delayed ratio-dependent prey–predator model within fluctuating environment. Appl. Math. Comput. 196, 458–478 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bandyopadhyay, M., Saha, T., Pal, R.: Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment. Nonlinear Anal. 2, 958–970 (2008)

    MathSciNet  MATH  Google Scholar 

  8. Kar, T.K.: Influence of environmental noises on the Gompertz model of two species fishery. Ecol. Model. 173, 283–293 (2004)

    Article  Google Scholar 

  9. Elsonbaty, A., Elsaid, A., Nour, H.M.: Effects of environmental fluctuation and time delay on ratio dependent hyperparasitism model. Commun. Nonlinear Sci. Numer. Simul. 16, 2609–2619 (2011)

  10. Mukhopadhyay, B., Bhattacharyya, R.: Role of gestation delay in a plankton-fish model under stochastic fluctuations. Math. Biosci. 215, 26–34 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Huang, D.W., Wang, H.L., Feng, J.F., Zhu, Z.W.: Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics. Chaos Solitons Fractals 27, 1072–1079 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Huang, Z.T., Yang, Q.G., Cao, J.F.: Stochastic stability and bifurcation for the chronic state in Marchuks model with noise. Appl. Math. Model. 35, 5842–5855 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhu, W.Q.: Nonlinear dynamics and control—Hamilton theoretical system frame. Science Press, Beijing (2003)

    Google Scholar 

  14. Fang, W.X.: The research of stochastic stability and bifurcation of non-linear economical period model. Tianjin University doctoral dissertation (2007)

  15. Ericksona, R.A., Presley, S.M., Allen, L.J.S., Long, K.R., Cox, S.B.: A stage-structured, Aedes albopictus population model. Ecol. Model. 221, 1273–1283 (2010)

    Article  Google Scholar 

  16. Jiao, J.J., Long, W., Chen, L.S.: A single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin. Nonlinear Anal. 10, 3073–3081 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by National Natural Science Foundation of China (61273008). The authors gratefully acknowledge the reviewers for their comments and suggestions that greatly improved the presentation of this work.

Author information

Authors and Affiliations

  1. Institute of Systems Science, Northeastern University, Shenyang, 110819, Liaoning, China

    Yue Zhang, Yan Zheng & Feng Zhao

  2. Plastic and Reconstructive Surgery, University Health Network, Toronto, ON, Canada

    Xi Liu

Authors
  1. Yue Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yue Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Y., Zheng, Y., Zhao, F. et al. Dynamical analysis in a stochastic bioeconomic model with stage-structuring. Nonlinear Dyn 84, 1113–1121 (2016). https://doi.org/10.1007/s11071-015-2556-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2556-5

Keywords

Search

Navigation