一类延迟Gompertz方程的数值解的振动性分析

阳倩; 王琦

doi:10.12052/gdutxb.190162

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一类延迟Gompertz方程的数值解的振动性分析

更新时间：2026-05-27

- 一类延迟Gompertz方程的数值解的振动性分析
- An Oscillation Analysis of Numerical Solution of A Class of Delayed Gompertz Equations
- 广东工业大学学报 2020年37卷第4期页码：69-74
- 作者机构：
  
  广东工业大学应用数学学院,广东,广州,510520
- 作者简介：
  
  阳倩(1997–)，女，硕士研究生，主要研究方向为常微分方程数值解的振动性
  王琦(1978–)，男，教授，主要研究方向为微分方程数值解，E-mail：bmwzwq@126.com
- 基金信息：
  
  广东省自然科学基金资助项目(2017A030313031)
- DOI：10.12052/gdutxb.190162
  中图分类号： O241
- 网络首发：2020-07-11，
  
  纸质出版：2020
- 稿件说明：
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阳倩, 王琦. 一类延迟Gompertz方程的数值解的振动性分析[J]. 广东工业大学学报, 2020, 37(4): 69-74.

Yang Qian, Wang Qi. An Oscillation Analysis of Numerical Solution of A Class of Delayed Gompertz Equations[J]. 2020, 37(4): 69-74.
阳倩, 王琦. 一类延迟Gompertz方程的数值解的振动性分析[J]. 广东工业大学学报, 2020, 37(4): 69-74. DOI： 10.12052/gdutxb.190162.

Yang Qian, Wang Qi. An Oscillation Analysis of Numerical Solution of A Class of Delayed Gompertz Equations[J]. 2020, 37(4): 69-74. DOI： 10.12052/gdutxb.190162.

摘要

Gompertz方程常用于描述种群动态和肿瘤生长

本文研究了一类延迟Gompertz方程的振动性。首先利用泰勒公式线性化该方程

再对线性方程应用线性

方法得到其差分格式。其次

运用振动理论分别分析线性化后的方程和所得差分格式。在研究方程数值解的振动性时

把差分方程中

的取值范围分为2部分

通过分析差分方程的特征方程的解的性质

得到延迟Gompertz方程的解析解和数值解振动的充分条件，最后进行数值实验验证。

Abstract

Oscillation of numerical solutions is studied with regard to a class of delayed Gompertz equations

which have been widely used in description of the population dynamics and tumour growth. Firstly

the linearized equations are obtained by Taylor formula and its corresponding difference equations by linear

method. Secondly

the oscillation theory is applied to analyze those obtained equations. In the process

the oscillation is primarily discussed through studying the properties of roots for the corresponding characteristic equations. For requirement

the oscillation of numerical solutions is discussed while the variable

belongs in different scopes. Accordingly

the sufficient conditions under which numerical solutions oscillate are acquired. To verify the results

some numerical experiments are given. The first three exper

iments validate the conditions of the delayed Gompertz equation which has three delay terms. And the rest of the experiments check on another which has two delay terms.

关键词

Keywords

references

HUANG M G, LUO J W, HU L C, et al . Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations [J ] . Journal of Theoretical Biology, 2018, 440: 1-11.

MISRA A K, RAI R K, TAKEUCHI Y. Modeling the effect of time delay in budget allocation to control an epidemic through awareness [J]. International Journal of Biomathematics, 2018, 11(2): 53-62.

SONG P F, XIAO Y N. Global hopf bifurcation of a delayed equation describing the lag effect of media impact on the spread of infectious disease [J]. Journal of Mathematical Biology, 2018, 76(5): 1249-1267.

LIU H J, ZHANG J F. Dynamics of two time delays differential equation model to HIV latent infection [J]. Physica A: Statistical Mechanics and Its Applications, 2019, 514: 384-395.

RAMEH R B, CHERRY E M, SANTOS R W. Single-variable delay-differential equation approximations of the Fitzhugh-Nagumo and Hodgkin-Huxley models [J]. Communications in Nonlinear Science and Numerical Simulation, 2020, 82: 105066-105077.

MITRA R K, BANIK A K, DATTA T K, et al . Nonlinear roll oscillation of semisubmersible system and its control [J ] . International Journal of Non-Linear Mechanics, 2018, 107: 42-55.

HU B, DIAO X, ZONG L Q, et al . The onset mechanism of Parkinson’s beta oscillations: a theoretical analysis [J ] . Journal of Theoretical Biology, 2019, 470: 1-16.

GRACE S R, GRAEF J R, JADLOVSKÁ I. Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms [J]. 0Mathematica Slovaca, 2019, 69(5): 1117-1126.

SONG F Y, GAO J F. Oscillation analysis of numerical solutions for a kind of nonlinear delay differential equation [J]. Acta Mathematicae Applicatae Sinica, 2016, 39(5): 762-773.

GAO J F. Numerical oscillation and non-oscillation for differential equation with piecewise continuous arguments of mixed type [J]. Applied Mathematics and Computation, 2017, 299: 16-27.

SANTRA S S. Necessary and sufficient conditions for oscillation to second-order half-linear delay differential equations [J]. Journal of Fixed Point Theory and Applications, 2019, 21(3): 85.

WANG Q, WEN J C, ZHANG P. Oscillation analysis of advertising capital model: analytical and numerical studies [J]. Applied Mathematics and Computation, 2019, 354: 365-376.

GOMPERTZ B. On the nature of the function expressive of the law of human mortality, and on the new mode of determining the value of life contingencies [J]. Philosophical Transactions of The Royal Society of London, 1825, 115: 513-585.

WINSOR C P. The Gompertz curve as a growth curve [J]. Proceedings of The National Academy of Sciences, 1932, 18(1): 1-8.

LAIRD A K, TYLER S A, BARTON A D. Dynamics of normal growth [J]. Growth, 1965, 29(3): 233-248.

PIOTROWSKA M J, FORYŚ U. The nature of Hopf bifurcation for the Gompertz model with delays [J]. Mathematical Computer Modelling, 2011, 54(9-10): 2183-2198.

BODNAR M, PIOTROWSKA M J, FORYŚ U. Gompertz model with delays and treatment: mathematical analysis [J]. Mathematical Biosciences and Engineering (Online), 2013, 10(3): 551-563.

CABRALES L E B, MONTIJANO J I, SCHONBEK M, et al . A viscous modified gompertz model for the analysis of the kinetics of tumors under electrochemical therapy [J ] . Mathematics and Computers in Simulation, 2018, 151: 96-110.

SONG J Z, WANG Y Y. Numerical bifurcation and hybrid control of a Gompertz model with time delay [J]. Journal of Hebei University of Science and Technology, 2019, 40(2): 112-118.

LEDZEWICZ U, MUNDEN J, SCHÄTTLER H. Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models [J]. Discrete and Continuous Dynamical Systems-Series B (DCDS-B), 2012, 12(2): 415-438.

ENDERLING H, CHAPLAIN M A J. Mathematical modeling of tumor growth and treatment [J]. Current Pharmaceutical Design, 2014, 20(30): 4934-4940.

LEDZEWICZ U, MAURER H, SCHÄTTLER H. Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy [J]. Mathematical Biosciences and Engineering (Online), 2017, 8(2): 307-323.

GYÖRI I, LADAS G. Oscillation theory of delay differential equations[M]. Oxford: Clarendon Press, 1991.

SONG M H, YANG Z W, LIU M Z. Stability of θ -methods for advanced differential equations with piecewise continuous arguments [J ] . Computers Mathematics with Applications, 2005, 49(9-10): 1295-1301.

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