Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method

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Abstract

The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopyanalysis method (HAM). The continuous solution for the nonlinear system is given, whichprovides a convenient and straightforward approach to calculate the dynamics of the system.The HAM continuous solution generated by polynomial base functions is of comparable accuracyto the purely numerical fourth-order Runge-Kutta method. The convergence theorem forthe three-dimensional case is also given.

Original languageEnglish
Article number816787
JournalDifferential Equations and Nonlinear Mechanics
Volume2008
DOIs
Publication statusPublished - 2008

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Lotka-Volterra Equations
Homotopy Analysis Method
Continuous Solution
Series Solution
Polynomial Basis
Lotka-Volterra System
Runge Kutta methods
Polynomial function
Runge-Kutta Methods
Convergence Theorem
Fourth Order
Basis Functions
Nonlinear systems
Nonlinear Systems
Polynomials
Calculate
Three-dimensional

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mechanics of Materials

Cite this

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abstract = "The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopyanalysis method (HAM). The continuous solution for the nonlinear system is given, whichprovides a convenient and straightforward approach to calculate the dynamics of the system.The HAM continuous solution generated by polynomial base functions is of comparable accuracyto the purely numerical fourth-order Runge-Kutta method. The convergence theorem forthe three-dimensional case is also given.",
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AB - The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopyanalysis method (HAM). The continuous solution for the nonlinear system is given, whichprovides a convenient and straightforward approach to calculate the dynamics of the system.The HAM continuous solution generated by polynomial base functions is of comparable accuracyto the purely numerical fourth-order Runge-Kutta method. The convergence theorem forthe three-dimensional case is also given.

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