Skip to main navigation menu Skip to main content Skip to site footer

Vol. 31 No. 1 (2026)

Applied Mathematics

On the dynamic of discrete-time Rayleigh-Duffing oscillators

https://doi.org/10.64785/mc.31.1.6

Published 2025-09-16

  • Mehdi Fatehi Nia
    • ,
  • Zehra Nurkanović
    • ,
  • Najmeh Khajoei

Mehdi Fatehi Nia
Department of Mathematics, Yazd University

Zehra Nurkanović
Department of Mathematics, University of Tuzla

Najmeh Khajoei
Department of Mathematics, Shahid Bahonar University of Kerman

Abstract

This paper investigates the dynamics of a discrete-time Rayleigh-Duffing oscillator exhibiting chaos in the Li-Yorke sense. We use Marotto's theorem to prove the existence of chaos by finding snap-back repeller. It is shown that the system undergoes a Neimark-Sacker bifurcation and a period-doubling bifurcation. We compute the Lyapunov exponents numerically to show sensitive dependence on initial conditions and chaotic behavior. The illustration of the results is presented using numerical simulations.

Keywords

Period-doubling bifurcation, Neimark-Sacker bifurcation, Lyapunov exponent, Marotto's method, Li-York chaos

PDF file

Supplementary File(s)

TEX file