HU Chun-hua.An Algorithm of Population Forecast with Fractional Derivative and Variational Iteration Method[J].Journal of Chengdu University of Information Technology,2017,(01):78-81.[doi:10.16836/j.cnki.jcuit.2017.01.013]
基于分数阶导数和变分迭代法的人口预测算法
- Title:
- An Algorithm of Population Forecast with Fractional Derivative and Variational Iteration Method
- 文章编号:
- 2096-1618(2017)01-0078-04
- 关键词:
- 应用数学; Logistic模型; Caputo导数; 拉普拉斯变换; 变分迭代法
- Keywords:
- applied mathematics; Logistic model; Caputo's fractional deriva-tive; Laplace transform; variationaliterationmethod.
- 分类号:
- O29Document
- 文献标志码:
- A
- 摘要:
- 通过对经典的Logistic模型进行修正,构造一种基于分数阶导数的人口预测算法。主要应用分数阶导数对带有收获函数的Logistic模型进行修正,将经典的Logistic模型修正为分数阶微分模型,再用变分迭代法解修正后的Logistic模型,由此可得到分数阶微分模型的各阶近似解。通过预测美国人口比较了带有收获函数的Logistic模型和分数阶Logistic模型的优缺点。通过比较发现,分数阶Logistic模型能更好的吻合实际数据,提高预测的精度。
- Abstract:
- An algorithm of population forecast is established by Caputo's fractional derivative,the fractional derivative was extended to modify the Logistic model with harvesting functions,and the variational iteration method is applied to find approximate solutions of the model with Caputo's fractional derivative.As an example of America population forecast,by comparing the Logisticmodel with harvesting function and the model with fractional derivative,the results of this paper are much closer to the actual situation than that obtained by the classical Logistic model.
参考文献/References:
[1] Zhao D,Yuan S.A note on persistence and extinction of arandomized food limited logistic population model[J].Appl.Math.Comput.2014,246:599-607.
[2] Idlango M A,Shepherd J J,Gear J A.On the multiscale approximation of solutions to the slowly varying harvested logistic population model[J].Commun.Nonlinear Sci.2015,26:36-44.
[3] Kovalchik S A,Matteis S D,Landi MT,et al.A regression model for risk difference estimation in population-based case-control studies clarifies gender differences in lung cancer risk of smokers and never smokers[J].Bmc Med.Res.Methodol.2013,13:119-124.
[4] Kondo T,Sagawa M,Tanita T,et al.On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample[J].J.Appl.Stat.2010,37:25-40.
[5] Momani S,Qaralleh R.Numerical approximations and padeapproximants for a fractional population growth model[J].Appl.Math.Model.2007,31:1907-1914.
[6] Lutz W,Sanderson W,Scherbov S.The end of world population growth[J].Nature.2001,412:543-545.
[7] Santos J P C D,Cardoso L C,Monteiro E,et al.A Fractional-Order Epidemic Model for Bovine Babesiosis Disease andTick Populations[J].Abstr.Appl.Anal.2015,(1):1-10.
[8] He J H.Variational iteration method-a kind of non-linear analytical technique:some examples[J].Int.J.Nonlin.Mech.1999,34:699-708.
[9] Podlubny I.Fractional Differential Equations[M],Academic press San Diego,1999.
[10] Wu G C,Baleanu D.Variational iteration method for the Burgers'Flow with fractional derivatives-New Lagrange multipliers[J].Appl.Math.Model.2013,37:6183-6190.
[11] Wu G C,Baleanu D.Variational iteration method for fractional calculus-a universal approach by Laplace transform[J].Adv.Differ.Equ(NY).2013,2013:18.
[12] Safuan H M,Jovanoski Z,Towers I N,et al.Exact solution of a non-autonomous logistic population model[J].Ecol.Model.2013,251:99-102.
[13] https://en.wikipedia.org/wiki/United States Cen-sus[EB/OL].
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备注/Memo
Received date:2016-04-26 Foundation item:Project Supported by the National Natural Science Foundation of China(11171046)