Skip to main content
SpringerLink
Log in

Dynamics of Modified Leslie-Gower Model with Stochastic Influences

  • Conference paper
  • First Online:
Advances in Computing and Data Sciences (ICACDS 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 906))

Included in the following conference series:

  • 862 Accesses

Abstract

The dynamics of modified Leslie-Gower prey-predator model exposed to stochastic influences are investigated in this paper. We inspect basic mathematical peculiarity of the proposed model such as positivity, boundedness of solution, Local stability of equilibrium point that exists in the system. The variation of population and the stability of the system about the positive equilibrium point controlled by the Gaussian white noise are computed. Finally, we effectuate the numerical simulation to illustrate the analytical findings.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Huo, H., Wang, X., Chavez, C.: Dynamics of a stage-structured Leslie-gower predator-prey model. Math. Probl. Eng 2011, 149341 (2011)

    Article  MathSciNet  Google Scholar 

  2. Leslie, P.H., Gower, J.C.: The properties of stochastic model for the predator-prey type of interaction between two species. Biometrika 47, 219–234 (1960)

    Article  MathSciNet  Google Scholar 

  3. Nindjin, A.F., Aziz-Alaoui, M.A.: Persistence and global stability in a delayed Leslie-Gower model with three species fochain. J. Math. Anal. Appl. 340(1), 340 (2013)

    Article  Google Scholar 

  4. Priyadarshi, A., Gakkar, S.: Dynamics of Leslie-gower type generalist predator in tri-trophic food web system. Commun. Nonlinear Sci. Simul. 18, 3202–3218 (2013)

    Article  MathSciNet  Google Scholar 

  5. Ruan, S., Xiao, D.: Global analysis in a prey-predator system with non-monotonic function functional response. SIAM J. Appl. Math. 61(4), 1445–1472 (2001)

    Article  Google Scholar 

  6. Shen, C.: Permanence and global attractivity of food chain system with holling type IV functional response. Appl. Math. Comput. 215, 179–185 (2009)

    MATH  Google Scholar 

  7. Sokol, W., Howell, J.A.: The kinetics of phenol oxidation by washed cells. Biotechnol. Bioeng. 30, 921–927 (1987)

    Article  Google Scholar 

  8. Upadhyay, R.K., Rsw, S.N.: Complex dynamics of a three species food chain model with holling type IV functional response. Nonlinear Anal. Model Control 16(3), 353–374 (2011)

    MathSciNet  MATH  Google Scholar 

  9. Upadhyay, R.K., Iyengar, S.R.K.: Introduction to Mathematical Modeling and Chaotic Dynamics. A Chapman and Hall Book. CRC Press, Boca Raton (2014)

    MATH  Google Scholar 

  10. Yu, S.: Global stability of a modified Leslie-Gower model with Beddington-DeAngelis functional response. Adv. Differ. Eqn. 2014, 84 (2014)

    Article  Google Scholar 

  11. Yue, Q.: Dynamics of a modified Leslie-Gower model with Holling Type II schemes and prey refuge. Springer Plus 5, 461 (2016)

    Article  Google Scholar 

  12. Yue, Q.: Permanence for a Leslie-gower model with beddington–DeAngelis functional response and feedback controls. Adv. Differ. Eq. 2015, 81 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, RIT, Chennai, Tamilnadu, India

    V. Nagaraju

  2. Department of Electronics and Communication Engineering, S.A. Engineering College, Chennai, Tamilnadu, India

    B. R. Tapas Bapu & S. Pradeep

  3. Department of Mathematics, S.A. Engineering College, Chennai, Tamilnadu, India

    V. Madhusudanan

Authors
  1. V. Nagaraju
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. R. Tapas Bapu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Pradeep
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. Madhusudanan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Madhusudanan .

Editor information

Editors and Affiliations

  1. University of KwaZulu-Natal, Durban, South Africa

    Mayank Singh

  2. Jaypee University of Information Technology, Solan, India

    P. K. Gupta

  3. Jaypee University of Engineering and Technology, Guna, Madhya Pradesh, India

    Vipin Tyagi

  4. Institute of Information Theory and Automation, Prague 8, Czech Republic

    Jan Flusser

  5. University of Ottawa, Ottawa, Canada

    Tuncer Ören

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Nagaraju, V., Tapas Bapu, B.R., Pradeep, S., Madhusudanan, V. (2018). Dynamics of Modified Leslie-Gower Model with Stochastic Influences. In: Singh, M., Gupta, P., Tyagi, V., Flusser, J., Ören, T. (eds) Advances in Computing and Data Sciences. ICACDS 2018. Communications in Computer and Information Science, vol 906. Springer, Singapore. https://doi.org/10.1007/978-981-13-1813-9_32

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-1813-9_32

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-1812-2

  • Online ISBN: 978-981-13-1813-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation