We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown.

This paper presents a dynamic connection that can induce amplitude death in globally coupled oscillators. A linear analysis clarifies a local stability condition for global amplitude death. The analysis also indicates that the odd-number property, which is known in delayed feedback control, exists in global dynamic coupled oscillators. Furthermore, global amplitude death is experimentally obser...

In undirected networks of identical linear oscillators coupled through dissipative and restorative connectors (e.g., pendulums undergoing small vibrations connected via dampers springs), the relation between asymptotic synchronization coupling structure is studied. Conditions on interconnection under which can be achieved for some selection strengths are established. How to strengthen those con...

In 2004, Kim and Chan (KC) reported a decrease in the period of torsional oscillators (TO) containing samples of solid (4)He, as the temperature was lowered below 0.2 K [Kim E, Chan MHW (2004) Science 305(5692):1941-1944]. These unexpected results constituted the first experimental evidence that the long-predicted supersolid state of solid (4)He may exist in nature. The KC results were quickly ...

Cluster synchronization modes of continuous time oscillators that are diffusively coupled in a three-dimensional (3-D) lattice are studied in the paper via the corresponding linear invariant manifolds. Depending in an essential way on the number of oscillators composing the lattice in three volume directions, the set of possible regimes of spatiotemporal synchronization is examined. Sufficient ...