Synchronisation

In this Chapter we derive a general framework to analyse the emergence of collective behaviour in any complex network of interacting phase-oscillators. Collective behaviour is ubiquitous. It appears spontaneously due to the interaction among the dynamical units composing a complex system and corresponds to an ordered state that can be absent in the dynamics of the individual units. Examples where collective behaviour are found include ecosystems, biological systems (as the brain or insect colonies), and even human societies and man-made systems (as the brain or insect colonies), and even human societies and man-made systems.

At the heart of the universe is a steady, insistent beat: the sound of cycles in sync. It pervades nature at every scale from the nucleus to the cosmos. Every night along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison, without any leader or cue from the environment. Trillions of electrons march in lockstep in a superconductor, enabling electricity to flow through it with zero resistance. [...] Even our bodies are symphonies of rhythm, kept alive by the relentless, coordinated firing of thousands of pacemaker cells in our hearts. In every case, these feats of synchrony occur spontaneously, almost as if nature has an eerie yearning for order
Taken from the book by Steven H. Strogatz Sync: The Emerging Science of Spontaneous Order, Hyperion books, New York, Preface 1st Ed. (2003).