Dynamic analysis of a fuzzy Bobwhite quail population model under g-division law

Abstract

This paper is concerned with a kind of Bobwhite quail population model xn+1=A+Bxn+xnxn-1xn-2,n=0,1,⋯,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} x_{n+1}=A+Bx_n+\\frac{x_n}{x_{n-1}x_{n-2}},\\ \\ n=0,1,\\cdots , \\end{aligned}$$\\end{document}where the parameters and initial values are positive parabolic fuzzy numbers. According to g-division of fuzzy sets and based on the symmetrical parabolic fuzzy numbers, the conditional stability of this model is proved. Besides the existence, boundedness and persistence of its unique positive fuzzy solution. When some fuzzy stability conditions are satisfied, the model evolution exhibits oscillations with return to a fixed fuzzy equilibrium no matter what the initial value is. This phenomena provided a vivid counterexample to Allee effect in density-dependent populations of organisms. As a supplement, two numerical examples with data-table are interspersed to illustrate the effectiveness. Our findings have been verified precise with collected northern bobwhite data in Texas, and will help to form some efficient density estimates for wildlife populations of universal applications.