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Two pendulums attached to a common support will eventually swing in opposite directions in perfect synchronization due to slight interactions between their motions.

A mathematical model used to describe synchronization. It consists of a set of coupled limit cycle oscillators with differing natural frequencies that tend to synchronize their phases while oscillating at a common frequency.

The process by which the frequency of one oscillator becomes adjusted to a precise ratio with the frequency of another due to coupling.

When coupled oscillators, under certain conditions, settle into a stable state and stop oscillating altogether.

A phenomenon where the presence of noise enhances the response of a dynamical system to a periodic input signal, often resulting in improved signal detection or transmission.

Oscillations that result from the incommensurable frequencies of interacting dynamical subsystems leading to a trajectory that fills a torus in the phase space, without any periodic repetition.

A closed trajectory in phase space toward which the system's trajectories converge from various initial conditions, representing a stable oscillatory motion of the system.

A dynamical phenomenon where a network of identical oscillators splits into coexisting regions of synchronous and incoherent oscillations.

A counterintuitive phenomenon where the introduction of noise into a system of coupled oscillators leads to a higher degree of synchronization amongst them.

The study of interconnected nodes or units that exhibit oscillatory behavior and are capable of complex patterns of synchronization and wave propagation.

Regions in parameter spaces where synchronization can occur for a given frequency ratio between two coupled oscillators.

A simple model of a driven oscillator where the dynamics can exhibit very rich behavior including quasiperiodicity, mode-locking, and chaotic dynamics.

A sequence of bifurcations that a coupled dynamical system undergoes which leads to a chaotic state, with sensitive dependence on initial conditions and aperiodic long-term behavior.

A phenomenon where two or more oscillators' phases become locked in a constant relationship due to interaction, so they oscillate at the same frequency.