In this paper, we study a second order rational difference equation. We analyze the stability of unique positive equilibrium equation and prove existence Neimark-Sacker bifurcation, validating our theoretical analysis via numerical exploration system.

A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2, . . . expresses a non-negative integer n as a sum n = ∑i j=0 ajuj . In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1, . . .) = g, then every sufficiently large multiple of g has some representation. If the lexicographic ordering on the representations is the ...