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Synchronization limit of weakly forced nonlinear oscillators
Hisa-Aki Tanaka
Journal of Physics A: Mathematical and Theoretical, Sep. 2014.
Keyword
synchronization, entrainment, injection-locking, fundamental limit, Arnold tongue, optimization, Holder's inequality
Abstract
Nonlinear oscillators exhibit synchronization (injection-locking) to external
periodic forcings, which underlies the mutual synchronization in networks of
nonlinear oscillators. Despite its history of synchronization and the practical
importance of injection-locking to date, there are many important open problems
of an efficient injection-locking for a given oscillator. In this work, I
elucidate a hidden mechanism governing the synchronization limit under weak
forcings, which is related to a widely known inequality; Holder's inequality.
This mechanism enables us to understand how and why the efficient injectionlocking
is realized; a general theory of synchronization limit is constructed
where the maximization of the synchronization range or the stability of synchronization
for general forcings including pulse trains, and a fundamental
limit of general m : n phase locking, are clarified systematically. These synchronization
limits and their utility are systematically verified in the Hodgkin?
Huxley neuron model as an example.
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