Abstract
According to a generalization of division (g-division) of fuzzy numbers, this paper is concerned with the boundedness, persistence and global behavior of a positive fuzzy solution of the third-order rational fuzzy difference equation $$x_{n+1}=A+\frac{x_{n}}{x_{n-1}x_{n-2}},\quad n=0,1,\ldots, $$ where A and initial values $x_{0}$ , $x_{-1}$ , $x_{-2}$ are positive fuzzy numbers. Moreover, some examples are given to demonstrate the effectiveness of the results obtained.
Highlights
It is well known that difference equations appear naturally as discrete analogs and as numerical solutions of differential equations and delay differential equations having many applications in economics, biology, computer science, control engineering, etc
There has been a lot of work concerning the global asymptotic stability, the periodicity, and the boundedness of nonlinear difference equations
In, Zhang et al [ ] investigated the global behavior for a system of the following third-order nonlinear difference equations: xn+
Summary
It is well known that difference equations appear naturally as discrete analogs and as numerical solutions of differential equations and delay differential equations having many applications in economics, biology, computer science, control engineering, etc. (see, for example, [ – ] and the references therein). There has been a lot of work concerning the global asymptotic stability, the periodicity, and the boundedness of nonlinear difference equations. Papaschinopoulos and Schinas [ ] investigated the global behavior for a system of the following two nonlinear difference equations: xn+ yn xn–p , yn+ xn yn–q. In , Yang [ ] studied the global behavior of the following system: xn yn– xn–pyn–q. Zhang et al Advances in Difference Equations (2015) 2015:108 where p ≥ , q ≥ , r ≥ , s ≥ , A is a positive constant, and initial values x –max{p,r}, x –max{p,r}, . In , Zhang et al [ ] investigated the global behavior for a system of the following third-order nonlinear difference equations: B+
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