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Keywords:
higher order difference equation; positive equilibrium; global attractivity; population model
higher order difference equation; positive equilibrium; global attractivity; population model
Summary:
Consider the following higher order difference equation \begin{equation*} x_{n+1}= a_n x_n+ b_n f( x_n) + c_nf(x_{n-k}), \ n=0, 1, \dots , \end{equation*} where $ f\colon [0, \infty ) \rightarrow [0, \infty ) $ is a continuous function with $f(x)>0$ for $x>0$, $\lbrace a_n\rbrace $ is a sequence in $(0,1)$, $\lbrace b_n\rbrace $ and $\lbrace c_n\rbrace $ are sequences in $[0,1)$ with $a_n+b_n+c_n=1$ and $a_n, b_n$ and $c_n$ are convergent, and $k$ is a positive integer. Our aim in this paper is to study the global attractivity of positive solutions of this equation and its applications.
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