Population dynamics between a prey and a predator using spectral collocation method  

作　　者：Sagithyn Thirumalai Rajeuwari Seshadri Suayip Yuzbasi 

机构地区：[1]Department of Mathematics,Pondicherry University,India [2]Department of Mathematicst Facviiy of Science Akdeniz University,Tr-07058,Antalya,Turkey

出　　处：《International Journal of Biomathematics》2019年第5期19-41,共23页生物数学学报（英文版）

摘　　要：The struggle for the existence of the biological species is a well-known Prey-Predator model study in the literature.In this study,we present an improved model of Jerri [J.Abdul,Introduction to Integral Equations with Applications,Vol.10 (Wiley,New York,1999)] by introducing the intra-species competition term between the same species in additiuu to the existing environmental changeb and lew other factors in the model.The derntmcl from the exiting (limited) retjources arid other requirements induces competition between the same species which may after the survival tactics among themselves.This intra species term provides strength to tho model ns it makes the model moro realistic.The governing equations are a system of two nonlinear delay integro differential pqimtions,which are solved using spectral collocation method.The role of intra-species coefficients denoting the logistic growth/decay of the two species and two other parameters affecting the population dynamics are analyzed with the three basis functions such as Chebyshev,Legendre and Jacobi polynomials.With the help of simple matrix analysis,the governing equations are converted into a system of nonlinear algebraic equations.Detailed error estiination is computed to compare our results witli the existing inethudb.It is shown with the help of tables and figures that the present method is very efficient,has better accuracy and has least computational cost.

关 键 词：PREY-PREDATOR model spectral COLLOCATION method Chebyshev  LEGENDRE and JACOBI polynomials error estimation 

分 类 号：G[文化科学]