Asymptotically periodic and bifurcation points in fractional difference maps

TL;DR

This paper derives analytic expressions for coefficients in equations used to identify asymptotically periodic and bifurcation points in fractional difference maps, aiding the analysis of their complex dynamics.

Contribution

It introduces explicit analytic formulas for coefficients in bifurcation equations, improving the calculation of asymptotically periodic points in fractional difference maps.

Findings

Derived explicit formulas for coefficients in bifurcation equations.

Enabled more accurate calculation of asymptotically periodic points.

Facilitated analysis of complex dynamics in fractional difference maps.

Abstract

The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived equations that allow calculations of asymptotically periodic and bifurcation points contain coefficients defined as slowly converging infinite sums. In this paper we derive analytic expressions for coefficients of the equations that allow calculations of asymptotically periodic and bifurcation points in fractional difference maps.