Discrete Logistic Growth Model with Capability to Go Backward in Time, Based on Successive Operations
DOI:
https://doi.org/10.5540/03.2022.009.01.0247Keywords:
Discrete Mathematics, Recursion, Successive Product, Successive Sum, Logistic Model.Abstract
his paper aims to tackle the classic discrete logistic model for population growth using the formalism of successive mathematical operations (see [1]-[2]). This approach allows obtaining a closed-form expression with the capability of retro-action for generations before the rst observed generation. Finally, to exemplify the advantages of this representation, it is used to compute the population size after and, outstandingly, before the reference, extending easily the usual discrete logistic growth model for all integer arguments.
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References
M. Moesia. Uma nova metodologia para a extensão de domínio de operações matemáticas sucessivas, com aplicações na análise combinatória.Master dissertation. Laboratório Nacional de Computação Científica, LNCC, 2017. ISBN: 978-85-923276-0-6 https://tede.lncc.br/handle/tede/256.
M. Moesia. A New Methodology for Domain Extension of the Mathematical Successive Operations. url: https://www.moesia.org.
P.F. Verhulst. Notice sur la loi que la population suit dans son accroissement. In: Correspondance Mathématique et Physique 10 (1838), pp. 113117.
J. D. Murray. Mathematical Biology. I. An Introduction. 2nd ed. Springer-Verlag, New York Inc., 1993, pp. 551. isbn: 0-387-95223-3.
R. M. May. Simple mathematical models with very complicated dynamics. In: Nature 261 (1976), pp. 459467.
M. Moesia, J. Karam-Filho, and G. A. Giraldi. Domain Extensions of Binomial Numbers Applying Successive Sums Transformations on Sequences Indexed by Integers. In: Trends in Applied and Computational Mathematics 21(1) (2020). https://tema.sbmac.org.br/ tema/article/download/1369/1006, pp. 133155. doi: 10.5540/tema.2020.021.01.133.
M. Moesia, J. Karam-Filho, and G. A. Giraldi. Successive Products Approach and its Application for Binomial Numbers Extensions from the Natural to the Integer Domain. In: Research Square Preprint (2022), pp. 139. doi: 10.21203/rs.3.rs-1392757/v1. url: https://doi.org/10.21203/rs.3.rs-1392757/v1.
Dan Kalman. A Discrete Approach to Continuous Logistic Growth. In: Contributed presentation at the Joint Mathematics Meetings. 2017, pp. 24. url: http : / / www . dankalman.net/AUhome/recent.html.
Dan Kalman. Elementary Mathematical Models Order a Plenty and a Glimpse of Chaos. Mineola, New York: The Mathematical Association of America, Inc., 1997, p. 362. isbn: 978-1-61444-601-9.
