Skip to main content

Dynamics of the Logistic Prey Predator Model in Crisp and Fuzzy Environment

  • Conference paper
  • First Online:
Mathematical Analysis and Applications in Modeling (ICMAAM 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 302))

Abstract

Recently the study of fuzzy dynamical system is growing rapidly in various field specially in biological system dynamics. In this article a dynamical model of two species population has been studied taking intrinsic growth rate, natural mortality rate and rate of conversion as triangular fuzzy number. Here the dynamics of the model system was discussed both in fuzzy and crisp environment. Also the analytical finding has been supported through numerical simulations.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Similar content being viewed by others

References

  1. Verhulst, P.F.: Notice sur la loi que la population suit dans son accroissement. Corresp. Math. Phys. 10, 113–121 (1838)

    Google Scholar 

  2. Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins, Baltimore (1925)

    MATH  Google Scholar 

  3. Volterra, V.: Lecons sur la theorie mathematique de la lutte pour la vie. Gauthier-Villars, Paris (1931)

    MATH  Google Scholar 

  4. Shih, S.D., Chow, S.S.: Equivalence of n-point Gauss-Chebyshev rule and 4n-point midpoint rule in computing the period of a Lotka-Volterra system. Adv. Comput. Math. 28, 63–79 (2008)

    Article  MathSciNet  Google Scholar 

  5. Liao, X., Chen, Y., Zhou, S.: Traveling wavefronts of a prey-predator diffusion system with stage-structure and harvesting. J. Comput. Appl. Math. 235, 2560–2568 (2011)

    Article  MathSciNet  Google Scholar 

  6. Qu, Y., Wei, J.: Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure. Nonlinear Dyn. 49, 285–294 (2007)

    Article  MathSciNet  Google Scholar 

  7. Seo, G., DeAngelis, D.L.: A predator-prey model with a Holling type I functional response including a predator mutual interference. J. Nonlinear Sci. 21, 811–833 (2011)

    Article  MathSciNet  Google Scholar 

  8. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  9. Bassanezi, R.C., Barros, L.C., Tonelli, A.: Attractors and asymptotic stability for fuzzy dynamical systems. Fuzzy Sets Syst. 113, 473–483 (2000)

    Article  MathSciNet  Google Scholar 

  10. Barros, L.C., Bassanezi, R.C., Tonelli, P.A.: Fuzzy modelling in population dynamics. Ecol. Model. 128, 27–33 (2000)

    Article  Google Scholar 

  11. Guo, M., Xu, X., Li, R.: Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets Syst. 138, 601–615 (2003)

    Article  MathSciNet  Google Scholar 

  12. Mizukoshi, M.T., Barros, L.C., Bassanezi, R.C.: Stability of fuzzy dynamic systems. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 17, 69–84 (2009)

    Article  MathSciNet  Google Scholar 

  13. Peixoto, M., Barros, L.C., Bassanezi, R.C.: Predator-prey fuzzy model. Ecol. Model. 214, 39–44 (2008)

    Article  Google Scholar 

  14. Pal, D., Mahaptra, G.S., Samanta, G.P.: Quota harvesting model for a single species population under fuzziness. IJMS 12(1–2), 33–46 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Alam .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tudu, S., Mondal, N., Alam, S. (2020). Dynamics of the Logistic Prey Predator Model in Crisp and Fuzzy Environment. In: Roy, P., Cao, X., Li, XZ., Das, P., Deo, S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore. https://doi.org/10.1007/978-981-15-0422-8_37

Download citation

Publish with us

Policies and ethics