Journal of Guangdong University of Technology ›› 2022, Vol. 39 ›› Issue (02): 62-65.doi: 10.12052/gdutxb.200125

Previous Articles     Next Articles

A Variational Iteration Method for Fractional Predator-Prey Model

Cen Da-kang, Wang Zhi-bo   

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2020-09-22 Online:2022-03-10 Published:2022-04-02

HTML

PDF (PC)

2345

Abstract: A variational iteration method (VIM) for a class of fractional predator-prey model is studied. A pair equivalent coupled integro-differential equation to the model is obtained by means of integral transformation. According to variational theory, the Lagrange multiplier is calculated and the VIM scheme is constructed. Finally, a convergence analysis of the scheme is given and a numerical simulation is carried out.The results verify the feasibility and effectiveness of the method.

Key words: fractional predator-prey model, variational iteration method, convergence

CLC Number: 

  • O241.8
[1] EAB C H, LIM S C. Fractional Langevin equations of distributed order [J]. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2011, 83(3): 031136.
[2] 赵天霄, 朱惠延, 刘岩柏, 等. 具水平抑制及母婴垂直传播的分数阶HIV/AIDS传染病模型的稳定性研究 [J]. 生物数学学报, 2018, 33(2): 204-210.
ZHAO T X, ZHU H Y, LIU Y B, et al, A study on stability of fractional HIV/ADIS epidemic model with horizontal inhibition and vertical mother-to-child transmission [J]. Journal of Biomathematics, 2018, 33(2): 204-210.
[3] DAS S. Functional fractional calculus [M]. Berlin: Springer, 2011.
[4] WANG Z, VONG S. Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation [J]. Journal of Computational Physics, 2014, 277: 1-15.
[5] 张会琴, 汪志波. 带周期边界的时间分数阶扩散方程的差分格式[J]. 广东工业大学学报, 2019, 36(3): 74-79.
ZHANG H Q, WANG Z B. Finite difference schemes for time fractional diffusion equations with periodic boundary conditions [J]. Journal of Guangdong University of Technology, 2019, 36(3): 74-79.
[6] HUANG C, STYNES M. Superconvergence of a finite element method for the multi-term time-fractional diffusion problem [J]. Journal of Scientific Computing, 2020, 82(1): 10.
[7] ZENG F, LI C, LIU F, et al. The use of finite difference/element approaches for solving the time-fractional subdiffusion equation [J]. SIAM Journal Scientific Computing, 2013, 35(6): A2979-A3000.
[8] INOKUTI M, SEKINE H, MURA T. General use of the Lagrange multiplier in nonlinear physics [J]. Variational Methods in the Mechanics of Solids, 1980: 156-162.
[9] HE J H. Variational iteration method for delay differential equation [J]. Communications in Nonlinear Science and Numerical Simulation, 1997, 2(4): 235-236.
[10] 尹伟石, 张绪财, 徐飞. 利用变分迭代法求Riesz分数阶偏微分方程近似解[J]. 黑龙江大学自然科学学报, 2016, 33(5): 587-591.
YIN W S, ZHANG X C, XU F. The approximate solution of Riesz fractional PDEs using variational iteration method [J]. Journal of Natural Science of Heilongjiang University, 2016, 33(5): 587-591.
[11] 高秀丽, 胡玉兰, 额尔敦布和. 基于变分迭代法数值模拟两种非线性发展方程的行波解[J]. 内蒙古大学学报(自然科学版), 2018, 49(6): 567-575.
GAO X L, HU Y L, EERDUN B. Numerical simulation of travelling wave solutions for mathematical physics equations by variational iteration method [J]. Journal of Inner Mongolia University (Natural Science Edition), 2018, 49(6): 567-575.
[12] 姜兆敏, 黄金城, 曹毅, 等. 利用变分迭代法解二阶常微分方程组边值问题 [J]. 数学的实践与认识, 2014, 44(10) : 289-293.
JIANG Z M, HUANG J C, CAO Y, et al, Numerical solutions of system of second-order boundary value problems using variational iteration method [J]. Mathematics in Practice and Theory, 2014, 44(10): 289-293.
[13] EL-SHAHED M, AHMED A M, ABDELSTAR I M E. Fractional order model in generalist Predator-Prey dynamics. [J]. International Journal of Mathematics and its Applications, 2016, 4(3-A): 19-28.
[14] 王虎, 田晶磊, 孙玉琴, 等. 具有阶段结构的时滞分数阶捕食者-食饵系统的稳定性分析[J]. 应用数学学报, 2018, 41(1): 27-42.
WANG H, TIAN J L, SUN Y Q, et al. Stability analysis of fractional stage-structured Predator-Prey system with delay [J]. Acta Mathematicae Applicatae Sinica, 2018, 41(1): 27-42.
[15] 汪维刚, 石兰芳, 莫嘉琪. 一类生态模型的近似解析解[J]. 武汉大学学报(理学版), 2015, 61(4): 315-318.
WANG W G, SHI L F, MO J Q. The approximate analytic solution of a class of ecological model [J]. Journal of Wuhan University (Natural Science Edition), 2015, 61(4): 315-318.
[1] Chen Ci, Xie Li-hua. A Data-Driven Prescribed Convergence Rate Design for Robust Tracking of Discrete-Time Systems [J]. Journal of Guangdong University of Technology, 2021, 38(06): 29-34.
[2] Zhang Hui-qin, Wang Zhi-bo. Finite Difference Schemes for Time Fractional Diffusion Equations with Periodic Boundary Conditions [J]. Journal of Guangdong University of Technology, 2019, 36(03): 74-79.
[3] Liu Yi, Zhang Yun. Convergence Condition of Value-iteration Based Adaptive Dynamic Programming [J]. Journal of Guangdong University of Technology, 2017, 34(05): 10-14.
[4] ZHOU Yu-Guang, ZENG Bi, YE Lin-Feng. Improved Particle Swarm Optimization and-Its Application in 4G Network Base Station Location [J]. Journal of Guangdong University of Technology, 2015, 32(2): 64-68.
[5] ZENG Shi-Kai, LI Li-Juan. Application of Improved Group Search Optimizer in Shape Optimization of Truss Structures [J]. Journal of Guangdong University of Technology, 2010, 27(2): 27-31.
[6] MO Hao-yi . Neural Network for a Kind of General Linear Complementarity Problem [J]. Journal of Guangdong University of Technology, 2007, 24(2): 20-23.
[7] HUI A-li~1,ZHENG Jian-ming~2,SUN Yu~1. A Closed-Loop PD-Type Iterative Learning Control Scheme for Nonlinear Systems and Its Convergence [J]. Journal of Guangdong University of Technology, 2006, 23(2): 42-47.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright © 2017 Journal of Guangdong University of Technology
Add：729 East Dongfeng RD., Guangzhou PRC. Postcode: 510090
Tel：020-37626653,020-37626139,020-37626396
Email：xbzrb@gdut.edu.cn
Supported:Beijing Magtech