Period doublings in coupled parametrically forced damped pendulums

Period doublings in coupled parametrically forced damped pendulums.

We study period doublings in N (N = 2, 3, 4, . . .) coupled parametrically forced damped pendulums by varying A (the amplitude of the external driving force) and c (the strength of coupling). With increasing A, the stationary point undergoes multiple period-doubling transitions to chaos. We first investigate the two-coupled case with N = 2. For each period-doubling transition to chaos, the crit...

Multiple transitions to chaos in a damped parametrically forced pendulum.

We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying ω0 (the natural frequency of the pendulum) and A (the amplitude of the external driving force). As A is increased, the SP will restabilize after its instability, destabilize again, and so ad infinitum for any given ω0. Its destabilizations (restabilizations) ...

On the Dynamics of Coupled Parametrically Forced Oscillators

It is well known that an autonomous dynamical system can have a stable periodic orbit, arising for example through a Hopf bifurcation. When a collection of such oscillators is coupled together, the system can display a number of phase-locked solutions which can be understood in the weak coupling limit by using a phase model. It is also well known that a stable periodic orbit can be found for a ...

Quasipatterns in parametrically forced systems.

We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism, which is robust and works with single-fre...

Parametrically Forced Surface Waves