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

  • S. Tudu
  • N. Mondal
  • S. AlamEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)


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.


Prey-predator Stability Graded mean value Fuzzy set 


  1. 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. 2.
    Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins, Baltimore (1925)zbMATHGoogle Scholar
  3. 3.
    Volterra, V.: Lecons sur la theorie mathematique de la lutte pour la vie. Gauthier-Villars, Paris (1931)zbMATHGoogle Scholar
  4. 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)MathSciNetCrossRefGoogle Scholar
  5. 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)MathSciNetCrossRefGoogle Scholar
  6. 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)MathSciNetCrossRefGoogle Scholar
  7. 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)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefGoogle Scholar
  9. 9.
    Bassanezi, R.C., Barros, L.C., Tonelli, A.: Attractors and asymptotic stability for fuzzy dynamical systems. Fuzzy Sets Syst. 113, 473–483 (2000)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Barros, L.C., Bassanezi, R.C., Tonelli, P.A.: Fuzzy modelling in population dynamics. Ecol. Model. 128, 27–33 (2000)CrossRefGoogle Scholar
  11. 11.
    Guo, M., Xu, X., Li, R.: Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets Syst. 138, 601–615 (2003)MathSciNetCrossRefGoogle Scholar
  12. 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)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Peixoto, M., Barros, L.C., Bassanezi, R.C.: Predator-prey fuzzy model. Ecol. Model. 214, 39–44 (2008)CrossRefGoogle Scholar
  14. 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

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Engineering Science and TechnologyHowrahIndia

Personalised recommendations