The Third Kind Of Chebyshev Wavelet Solutions For Two Types Of Fractional Ecosystem Mathematical Models

In recent years,the frequent occurrence of imbalanced natural ecology,hunting and environmental pollution has not only led to the dilemma of the extinction of various bio-logical populations,but also has seriously affected the developing pace of social production and social life.Therefore,the ecosystem model research has received much attention.With the continuous promotion and improvement of ecological models,it has been found that fractional-scale ecosystem models are based on flexible variability of orders and provide reasonable explanations for the development and changes of systems in different situation-s.Above all,numerical simulation and the analysis of this model have important practi-cal significance.It is particularly critical to seek efficient numerical solutions because the fractional-order ecosystem model is difficult to find exact solutions.The third Chebyshev wavelet not only efficiently solves singular integral equations with singularities at intervals,but also shows high efficiency for solving nonsingular calculus equations.This thesis focuses on the third kind of Chebyshev wavelet solutions from two types of ecosystem mathematical models.Chapter 1 introduces the development background and research significance of these models and wavelet methods and briefly sketches out the re-search progress of these models at home and abroad.In Chapter 2,the product operator matrix and fractional-order integral operator matrix are deduced based on the definition and related theoretical knowledge and properties of Chebyshev wavelet.In Chapter 3,nonlinear fractional-order single population growth model is solved by wavelet and nonlinear fraction-al logistic population growth model.The non-linear fractional Volterra population growth model and the non-linear fractional Logistic population growth model are taken as exam-ples in the solving process.Firstly,the discrete form of the model is deduced by using the wavelet operator matrix.Secondly,the content error relationship of the model is defined and proved.Finally,a numerical example is respectively given to verify the practicability and effectiveness of the method.Chapter 4 considers the third kind of Chebyshev wavelet method for nonlinear fractional-order interaction systems and takes variable coefficient non-linear fractional Lotka-Volterra predator-prey model and nonlinear fractional lake pollution model as examples.Firstly,the model discrete format is deduced by the wavelet operator matrix and then the content error relationship is defined and proved.Finally high accuracy and feasibility of the method are proved by numerical examples in this thesis.The chapter 5 summarizes and outlooks the paper work and the inadequacies of the thesis.