Asymptotically period doubling bifurcation of fractional difference equations

Hu-Shuang Hou, Guo-Cheng Wu, René Lozi and Zhi-Wen Mo

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 982-999

Abstract: Nonlinear dynamics of fractional difference equations have recently received much attention. This paper investigates asymptotically period doubling bifurcation. By theories of discrete fractional calculus, the existence conditions for asymptotically period-2 and −4 cycles of fractional difference equations are given. New numerical schemes are employed to determine critical values. Finally, the fractional Hénon map is used as a high-dimensional example. It can be concluded that this paper provides a way of understanding the route to chaos in fractional difference equations.

Keywords: Fractional difference equations; Period doubling bifurcation; Asymptotically period-2 cycle; Asymptotically period-4 cycle (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:982-999

DOI: 10.1016/j.matcom.2025.08.017

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