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Global asymptotic stability for quadratic fractional difference equation (2015)

Mark Di; Pippo; Ed Janowski; Mustafa Kulenovi¿

SpringerOpen

In: Advances in Difference Equations

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Publication Date: 2015-06-13

Description: Consider the difference equationx n + 1 = α + ∑ i = 0 k a i x n − i + ∑ i = 0 k ∑ j = i k a i j x n − i x n − j β + ∑ i = 0 k b i x n − i + ∑ i = 0 k ∑ j = i k b i j x n − i x n − j , n = 0 , 1 , … ,where all parameters α, β, a i , b i , a i j , b i j , i , j = 0 , 1 , … , k , and the initial conditions x i , 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.MSC: 39A10, 39A30, 65L20.

Print ISSN: 1687-1839

Electronic ISSN: 1687-1847

Topics: Mathematics

Published by SpringerOpen

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