On the Dynamics of the Recursive Sequence

Abstract

Our aim in this paper is to investigate the local stability of the positive solutions of the difference equation

y_n+1= [(α-y_n)/ (βy_n-1)] − [(γ-y_n-1)/ βy_n ] ,  n=0,1,2,...,

where the initial conditions  y₋₁ ,  y₀ are arbitrary positive real numbers such that  y_n ≠ 0 for n= −1,0,1,...,  , α, β, γ ε (0,∞)  and α > γ. Furthermore we investigate the periodic nature of the mentioned difference equation.

Key Words: Difference Equations, Local Stability, Period-two Solutions.

 

Keywords

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References

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