Synchronization of coupled oscillators

4 problems

• Lifetime of chimera states in finite oscillator networks

  Partially resolved

  A chimera state is a pattern in which identical oscillators split into a synchronized group and an unsynchronized group. In infinite systems it can last forever, but in finite ones it eventually collapses, and how its lifetime grows with size is known only numerically.

• Finite-size scaling at the Kuramoto synchronization transition

  Partially resolved

  In a finite population of oscillators the sharp synchronization transition is smeared, and how the smearing shrinks with population size reveals its universality class. Different ways of choosing the oscillator frequencies give different answers.

• Lower critical dimensions for synchronization on lattices

  Contested

  When each oscillator is coupled only to its neighbors on a lattice and natural frequencies are random, synchronization may be impossible in low dimensions. The dimensions above which frequency locking and full phase locking can occur are not established.

• Existence of an oscillator glass in randomly coupled phase oscillators

  Open

  If oscillators are coupled with random signs, like spins in a spin glass, they may freeze into a disordered locked pattern, an oscillator glass. A peculiar transition seen in simulations in 1992 suggested this, but whether a true glass phase exists is unknown.