Solution and Attractivity for a Rational Recursive Sequence - E. M. Elsayed (Discrete Dynamics in Nature and Society)
This paper is concerned with the behavior of solution of the nonlinear difference equation 𝑥𝑛+1=𝑎𝑥𝑛−1+𝑏𝑥𝑛𝑥𝑛−1/(𝑐𝑥𝑛+𝑑𝑥𝑛−2), 𝑛=0,1,…, where the initial conditions 𝑥−2, 𝑥−1, 𝑥0 are arbitrary positive real numbers and 𝑎,𝑏,𝑐,𝑑 are positive constants. Also, we give specific form of the solution of four special cases of this equation.