Global behavior of a fourth-order difference equation with quadratic term

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of solutions of the difference equation: x n + 1 = a x n x n - 2 - b x n + c x n - 3 , n = 0 , 1 , … where a ,  b ,  c are positive real numbers and the initial conditions...

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Bibliographic Details
Published inBoletín de la Sociedad Matemática Mexicana Vol. 25; no. 1; pp. 187 - 194
Main Author Abo-Zeid, R.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 11.03.2019
Springer Nature B.V
Subjects
Difference equations
Fractals
Initial conditions
Mathematics
Mathematics and Statistics
Original Article
Real numbers
39A11
Difference equation
Periodic solution
Forbidden set
Unbounded solution
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Summary:In this paper, we determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of solutions of the difference equation: x n + 1 = a x n x n - 2 - b x n + c x n - 3 , n = 0 , 1 , … where a ,  b ,  c are positive real numbers and the initial conditions x - 3 , x - 2 , x - 1 , x 0 are real numbers.
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-017-0180-8