Multistability of Globally Coupled Duffing Oscillators

We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized clusters, as a consequence of the bistability of individual oscillators. The multiplicity of these solutions, induced by the many possible ways of distributing the oscillators between the two clusters, implies that the ensemble can exhibit multistability. As the strength of coupling grows, however, the two-cluster solutions are replaced by a state of full synchronization. By a combination of analytical and numerical techniques, we study the existence and stability of two-cluster solutions. The role of the distribution of oscillators between the clusters and the relative prevalence of the two stable solutions are disclosed.

Vibration control of coupled Duffing oscillators in flexible single-link manipulators

Motion-induced oscillations of the flexible single link and its payload at the tip have negative impact on the anticipated performance of the flexible manipulators and thus should be suppressed to achieve tip positioning accuracy and high-speed operation. Because of the structural flexibility, the dynamics of the flexible manipulator can be described by coupled Duffing oscillators when considering the inherent structural nonlinearity of the flexible link into the dynamic modeling. However, little research has been focused on addressing the dynamic coupling issue in the nonlinear modeling of flexible-link manipulators using coupled Duffing oscillators. This article presents coupled Duffing oscillators for the nonlinear modeling of flexible single-link manipulators and then proposes a control method for suppressing the nonlinear vibrations of the coupled Duffing oscillators. Simulated and experimental results obtained from a flexible single-link manipulator test bench are in good agreement with the proposed nonlinear modeling and also demonstrate the effectiveness of the proposed control techniques for vibration suppression of the flexible manipulator.

Stability of the 3-torus solution in a ring of coupled Duffing oscillators

The dynamics of the ring of unidirectionally coupled single-well Duffing oscillators is analyzed in numerical simulation for identical nodal oscillators. The research is concentrated on the existence of the stable 3D torus attractor in this system. It is shown that 3-frequency quasi-periodicity can be robustly stable in wide range of parameters of the system under consideration. As an explanation of this stability, the conjecture on the coexistence and superposition of two independent effects characterized with irrational frequencies, i.e., the classical Newhouse, Ruelle and Takens scenario and rotating wave flow, is formulated.