Abstract
Synchronization is described within the Nambu mechanics framework in order to take advantage of the fact that the evolution of a Nambu mechanics system is characterized by its invariants of motion. To this end, the canonical-dissipative approach to Nambu systems developed in earlier work is applied. A four-variable Nambu system is examined that describes synchronization between a pair of oscillators, each oscillator living in a two-dimensional phase space. The canonical part of the Nambu system exhibits three invariants and feature neutrally stable closed orbits. The canonical-dissipative generalization of the canonical part exhibits stable limit cycles in the four-variable phase space and projected limit cycles in the two-dimensional subspaces of the two oscillators.
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