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.
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References
Verhulst, P.F.: Notice sur la loi que la population suit dans son accroissement. Corresp. Math. Phys. 10, 113–121 (1838)
Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins, Baltimore (1925)
Volterra, V.: Lecons sur la theorie mathematique de la lutte pour la vie. Gauthier-Villars, Paris (1931)
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)
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)
Qu, Y., Wei, J.: Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure. Nonlinear Dyn. 49, 285–294 (2007)
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)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Bassanezi, R.C., Barros, L.C., Tonelli, A.: Attractors and asymptotic stability for fuzzy dynamical systems. Fuzzy Sets Syst. 113, 473–483 (2000)
Barros, L.C., Bassanezi, R.C., Tonelli, P.A.: Fuzzy modelling in population dynamics. Ecol. Model. 128, 27–33 (2000)
Guo, M., Xu, X., Li, R.: Impulsive functional differential inclusions and fuzzy population models. Fuzzy Sets Syst. 138, 601–615 (2003)
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)
Peixoto, M., Barros, L.C., Bassanezi, R.C.: Predator-prey fuzzy model. Ecol. Model. 214, 39–44 (2008)
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)
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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
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DOI: https://doi.org/10.1007/978-981-15-0422-8_37
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