Remarks on nonlinear dynamics of a suspension bridge model a note on fractional order

Abstract

This paper aims to explore the richer dynamics of the Lazer-McKenna suspension bridge model, which is a asymmetric system of equations that has previously shown chaotic dynamics, here the study will be made by means of fractional order differential equations where the order of the entire system is varied. For the solutions it was used integration schemes previously shown in the literature, which were implemented in the Python programming language, the dynamics were then analyzed in the time domain by means of phase-space, Poincare sections, and bifurcation diagrams, and in the frequency domain by Discrete Fourier Transform (DFT), ContinuousWavelet Transform (CWT) and Hilbert-Huang Transform (HHT). The investigated responses demonstrated a great influence of the fractional order in the system, changing its time dynamics from chaotic to periodic.