On the global stability of the nonlinear difference equation xn+1 = α0xn+α1xn−l+α2xn−m+α3xn−k β0xn+β1xn−l+β2xn−m+β3xn−k
نویسنده
چکیده
The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation xn+1 = α0xn + α1xn−l + α2xn−m + α3xn−k β0xn + β1xn−l + β2xn−m + β3xn−k , n = 0, 1, 2, · · · where the coefficients αi, βi ∈ (0,∞) for i = 0, 1, 2, 3, and l,m, k are positive integers. The initial conditions x−k,...,x−m,...,x−l, ...,x−1, x0 are arbitrary positive real numbers such that l < m < k. Some numerical experiments are presented. Key–Words: Difference equations, boundedness, period two solutions, convergence, global stability.
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