  Nonlinear dynamics emerge through either nonlinear interactions between the
variables or through nonlinearities imposed on their linear interactions. Their
interactions can be conceptualized as modulations of input-output (I/O)
functions, where one variable modulates another variable's I/O function. Within
this framework, nonlinear interactions are manifested as gain modulations,
where the gain (i.e. slope) of a variable's I/O function is modulated by
another variable. By analyzing oscillatory dynamics in modulation phase space,
I show that gain modulation qualitatively enhances phase plasticity by
loosening the relationship between oscillation phase and instantaneous gain.
This finding reveals how gain modulation renders nonlinear dynamics more
adaptable. I discuss the direct implications of this finding on the ability of
any nonlinear system to get entrained to rhythmic input and synchronize with
other systems and how it relates to neural dynamics.
