Nonlinearity induces an exponentially small phase shift in Van der Pol's equation that couples the slow and fast scales in multiple-scale expansions.
2015 Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice.SIAM Journal on Applied Dynamical Systems14, 481–521
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On the independence of the slow and fast scales in multiple-scale expansions, with application to Van der Pol's equation
Nonlinearity induces an exponentially small phase shift in Van der Pol's equation that couples the slow and fast scales in multiple-scale expansions.