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Dynamical behaviors of a k-order fuzzy difference equation
- Source :
- Open Mathematics, Vol 20, Iss 1, Pp 391-403 (2022)
- Publication Year :
- 2022
- Publisher :
- De Gruyter, 2022.
-
Abstract
- Difference equations are often used to create discrete mathematical models. In this paper, we mainly study the dynamical behaviors of positive solutions of a nonlinear fuzzy difference equation: xn+1=xnA+Bxn−k(n=0,1,2,…),{x}_{n+1}=\frac{{x}_{n}}{A+B{x}_{n-k}}\hspace{0.33em}\left(n=0,1,2,\ldots ), where parameters A,BA,B and initial value x−k,x−k+1,…,x−1,x0{x}_{-k},{x}_{-k+1},\ldots ,{x}_{-1},{x}_{0}, k∈{0,1,…}k\in \{0,1,\ldots \} are positive fuzzy numbers. We investigate the existence, boundedness, convergence, and asymptotic stability of the positive solutions of the fuzzy difference equation. At last, we give numerical examples to intuitively reflect the global behavior. The conclusion of the global stability of this paper can be applied directly to production practice.
Details
- Language :
- English
- ISSN :
- 23915455
- Volume :
- 20
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Open Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.12959f2688694033b51e6ef2db6d0957
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/math-2022-0020