Epistemology

Coupling (piping)

Mathematical analysis

Engineering

Philosophy

Artificial intelligence

Complex network

Combinatorics

Physics

Work (physics)

Dynamical systems theory

Topology (electrical circuits)

Mathematics

Complex system

Quantum mechanics

Computer science

Statistical physics

World Wide Web

Synchronization (alternating current)

Simple (philosophy)

Synchronization networks

Complex dynamics

Mechanical engineering

Science

Synchronization of oscillators, a phenomenon found in a wide variety of natural and engineered systems, is typically understood through a reduction to a first-order phase model with simplified dynamics. Here, by exploiting the precision and flexibility of nanoelectromechanical systems, we examined the dynamics of a ring of quasi-sinusoidal oscillators at and beyond first order. Beyond first order, we found exotic states of synchronization with highly complex dynamics, including weak chimeras, decoupled states, traveling waves, and inhomogeneous synchronized states. Through theory and experiment, we show that these exotic states rely on complex interactions emerging out of networks with simple linear nearest-neighbor coupling. This work provides insight into the dynamical richness of complex systems with weak nonlinearities and local interactions.

Exotic states in a simple network of nanoelectromechanical oscillators