Document Type

Article

Date of Original Version

6-12-2015

DOI

10.1186/s13662-015-0525-4

Abstract

Consider the difference equation

xn+1=((α+∑ki=0aixn−i+∑ki=0∑kj=iaijxn−ixn−j)/(β+∑ki=0bixn−i+∑ki=0∑kj=ibijxn−ixn−j)),n=0,1,…,

where all parameters α, β,ai,bi,aij,bij,i,j=0,1,…,k, and the initial conditions xi,i∈{−k,…,0}, are nonnegative. We investigate the asymptotic behavior of the solutions of the considered equation. We give simple explicit conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

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