Experiments on the bifurcation behaviour of a forced nonlinear pendulum

Experimental and numerical investigation of chaotic regions in the triple physical pendulum

“…Many researchers have been actively investigating the complex responses of the system numerically. Beckert et al [2] studied a forced nonlinear torsion pendulum by measuring a bifurcation diagram, which showed period doubling to chaos. Blackburn et al [3] reported experimental observations of chaos in a driven, damped pendulum in which steady and alternating torques were applied.…”

Internal clocks induced by generating functions

“… The feedback operator F defined through the operation meaning that, by applying F to a function , it transforms it into the nonlinear functional . is a nonlinear term, such as a pendulum term [16] or Duffing term, [17] . In contrast to a linear oscillator, which can oscillate only with a single or discrete set of resonance frequencies, adding the nonlinear term F allows fine-tuning the frequencies.…”

“…Following from the self-organization models, our model consists of nonlinear equations. In particular, we demonstrate our approach with nonlinear classical mechanical systems, such as the damped, driven pendulum [16] or the Duffing equation [17] . In our model, the system is divided into sectors: each sector is associated with a nonlinear equation.…”

Phase Shadows: An Enhanced Representation of Nonlinear Dynamic Systems

“…Also, in other physical realms, it appears that different oscillators can be easily modeled as pendulum-like systems [Blackburn et al, 1987] or show dynamic behavior resembling pendulums [Ruelas & Rand, 2015]. Most efforts in this work have focused on the existence of bifurcations [Beckert et al, 1985], the study of chaotic behavior [Han et al, 2013], or both [Kameoka & Miyashita, 2003].…”