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Global Stability of a Second-Order Exponential-Type Difference Equation

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In this work, we explore the boundedness and local and global asymptotic behavior of the solutions to a second-order difference formula of the exponential type ξn+1=a+bξn−1+cξn−1e−ρξn, where a,c,ρ∈(0,∞), b∈(0,1) and… Click to show full abstract

In this work, we explore the boundedness and local and global asymptotic behavior of the solutions to a second-order difference formula of the exponential type ξn+1=a+bξn−1+cξn−1e−ρξn, where a,c,ρ∈(0,∞), b∈(0,1) and the initials ξ0,ξ−1 are non-negative real numbers. Some other special cases are given. We provide two concrete numerical examples to confirm the theoretical results.

Keywords: exponential type; difference; global stability; second order

Journal Title: Symmetry
Year Published: 2022

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