The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model
are studied using a phase dynamics approach. A Cross-Newell phase equation
describing slow and weak modulations of periodic stationary solutions is de
rived. The derivation applies to the bistable, excitable, and Turing unstab
le regimes. In the bistable case stability thresholds are obtained for the
Eckhaus and zigzag instabilities and for the transition to traveling waves.
Neutral stability curves demonstrate the destabilization of stationary pla
nar patterns at low wave numbers to zigzag and traveling modes. Numerical s
olutions of the model system support the theoretical findings.