Large time behavior of solution to second-order fractal difference equation with positive fuzzy parameters

Article type: Research Article

Authors: Zhang, Qianhong^{a; *} | Pan, Bairong^a | Ouyang, Miao^b | Lin, Fubiao^a

Affiliations: [a] School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, P. R. China | [b] School of Applied Mathematics, Xiamen University of Technology, Xiamen, Fujian, China

Correspondence: [*] Corresponding author. Qianhong Zhang, School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550025, P. R. China. Tel. +86 851 88510724, Fax. +86 851 88510724, E-mail: [email protected].

Abstract: The article is concerned with large time behavior of solution to second-order fractal difference equation with positive fuzzy parameters xn+1=A+xnB+xn-1,  n=1,2,⋯, here the initial values xi (i = -1, 0) and the parameters A, B are positive fuzzy numbers. Utilizing a generalization of division (g-division) of fuzzy numbers, one presents large time behaviors of positive fuzzy solution including persistence, boundedness, global convergence. Moreover, two numerical examples verify the effectiveness of the qualitative analysis.

Keywords: Second- order fractal difference equation, g-division, large time behavior, positive fuzzy parameter

DOI: 10.3233/JIFS-224099

Journal: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 4, pp. 5709-5721, 2023