Dynamics of a rational difference equation

Abstract

The authors investigate the global behavior of the solutions of the difference equation $x_{n + 1} = \frac{{ax_{n - l} x_{n - k} }}{{bx_{n - p} + cx_{n - q} }}, n = 0, 1, \cdots ,$ where the initial conditions x _−r, x _−r+1, x_−r+2, …, x ₀ are arbitrary positive real numbers, r = max{l, k, p, q} is a nonnegative integer and a, b, c are positive constants. Some special cases of this equation are also studied in this paper.

Keywords

Stability / Periodic solutions / Difference equations

References

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