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

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 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.

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

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

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

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

A sequence of interconnected oscillators where the dynamics of each one is influenced by its neighbors, leading to wave-like behavior or synchronization patterns.

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.

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.