Research article Special Issues

Periodic functions related to the Gompertz difference equation

  • Received: 11 May 2022 Revised: 31 May 2022 Accepted: 06 June 2022 Published: 17 June 2022
  • We investigate periodicity of functions related to the Gompertz difference equation. In particular, we derive difference equations that must be satisfied to guarantee periodicity of the solution.

    Citation: Tom Cuchta, Nick Wintz. Periodic functions related to the Gompertz difference equation[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 8774-8785. doi: 10.3934/mbe.2022407

    Related Papers:

  • We investigate periodicity of functions related to the Gompertz difference equation. In particular, we derive difference equations that must be satisfied to guarantee periodicity of the solution.



    加载中


    [1] M. Bohner, A. Peterson, Dynamic equations on time scales, An introduction with applications, Birkhäuser Boston, Inc., Boston, MA, 2001. https://doi.org/10.1007/978-1-4612-0201-1
    [2] S. G. Georgiev, K. Zennir, Boundary Value Problems on Time Scales, Volume I, Chapman and Hall/CRC, 2021. https://doi.org/10.1201/9781003173557
    [3] S. G. Georgiev, K. Zennir, Boundary Value Problems on Time Scales Volume II, Chapman and Hall/CRC, 2021. https://doi.org/10.1201/9781003175827
    [4] T. Cuchta, S. Streipert, Dynamic Gompertz model, Appl. Math. Info. Sci., 14 (2020), 1–9. https://doi.org/10.18576/amis/140102 doi: 10.18576/amis/140102
    [5] T. Cuchta, B. Fincham, Some new Gompertz fractional difference equations, Involve, 13 (2020), 705–719. https://doi.org/10.2140/involve.2020.13.705 doi: 10.2140/involve.2020.13.705
    [6] F. M. Atıcı, M. Atıcı, M. Belcher, D. Marshall, A new approach for modeling with discrete fractional equations, Fundam. Inform., 151 (2017), 313–324. https://doi.org/10.3233/FI-2017-1494 doi: 10.3233/FI-2017-1494
    [7] T. Cuchta, R. J. Niichel, S. Streipert, A Gompertz distribution for time scales, Turk. J. Math., 45 (2021), 185–200. https://doi.org/10.3906/mat-2003-101 doi: 10.3906/mat-2003-101
    [8] E. Akın, N. N. Pelen, I. U. Tiryaki, F. Yalcin, Parameter identification for Gompertz and logistic dynamic equations, PLOS ONE, 15 (2020), e0230582. https://doi.org/10.1371/journal.pone.0230582
    [9] G. Albano, V. Giorno, P. Román-Román, S. Román-Román, J. J. Serrano-Pérez, F. Torres-Ruiz, Inference on an heteroscedastic Gompertz tumor growth model, Math. Biosci., 328 (2020), 108428. https://doi.org/10.1016/j.mbs.2020.108428 doi: 10.1016/j.mbs.2020.108428
    [10] C. Vaghi, A. Rodallec, R. Fanciullino, J. Ciccolini, J. P. Mochel, M. Mastri, et al., Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors, PLoS Comput. Biol., 16 (2020), e1007178. https://doi.org/10.1371/journal.pcbi.1007178 doi: 10.1371/journal.pcbi.1007178
    [11] L. Zhang, Z. D. Teng, The dynamical behavior of a predator-prey system with Gompertz growth function and impulsive dispersal of prey between two patches, Math. Meth. Appl. Sci., 39 (2015), 3623–3639. https://doi.org/10.1002/mma.3806 doi: 10.1002/mma.3806
    [12] M. Nagula, Forecasting of fuel cell technology in hybrid and electric vehicles using Gompertz growth curve, J. Stat. Manage. Syst, 19 (2016), 73–88. https://doi.org/10.1080/09720510.2014.1001601 doi: 10.1080/09720510.2014.1001601
    [13] A. Sood, G. M. James, G. J. Tellis, J. Zhu, Predicting the path of technological innovation: SAW vs. Moore, Bass, Gompertz, and Kryder, Mark. Sci., 31 (2012), 964–979. https://doi.org/10.1287/mksc.1120.0739 doi: 10.1287/mksc.1120.0739
    [14] P. H. Franses, Gompertz curves with seasonality, Technol. Forecast. Soc. Change, 45 (1994), 287–297. https://doi.org/10.1016/0040-1625(94)90051-5 doi: 10.1016/0040-1625(94)90051-5
    [15] E. Pelinovsky, M. Kokoulina, A. Epifanova, A. Kurkin, O. Kurkina, M. Tang, et al., Gompertz model in COVID-19 spreading simulation, Chaos Solit. Fractals, 154 (2022), 111699. https://doi.org/10.1016/j.chaos.2021.111699 doi: 10.1016/j.chaos.2021.111699
    [16] R. A. Conde-Gutiérrez, D. Colorado, S. L. Hernández-Bautista, Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México, Nonlinear Dyn., 2021. https://doi.org/10.1007/s11071-021-06471-7
    [17] M. Bohner, G. S. Guseinov, B. Karpuz, Properties of the Laplace transform on time scales with arbitrary graininess, Integral Transforms Spec. Funct., 22 (2011), 785–800. https://doi.org/10.1080/10652469.2010.548335 doi: 10.1080/10652469.2010.548335
    [18] M. Bohner, G. S. Guseinov, B. Karpuz, Further properties of the Laplace transform on time scales with arbitrary graininess, Integral Transforms Spec. Funct., 24 (2013), 289–301. https://doi.org/10.1080/10652469.2012.689300 doi: 10.1080/10652469.2012.689300
    [19] M. Bohner, T. Cuchta, S. Streipert, Delay dynamic equations on isolated time scales and the relevance of one-periodic coefficients, Math. Meth. Appl. Sci., 45 (2022), 5821–5838. https://doi.org/10.1002/mma.8141 doi: 10.1002/mma.8141
    [20] M. Bohner, J. Mesquita, S. Streipert, Periodicity on isolated time scales, Math. Nachr., 295 (2022), 259–280. https://doi.org/10.1002/mana.201900360 doi: 10.1002/mana.201900360
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1305) PDF downloads(75) Cited by(0)

Article outline

Figures and Tables

Figures(2)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog