This work investigates the characteristics of brain interactions of experienced Zen-Buddhist practitioners by obtaining multichannel EEG (electroencephalogram) data. Brain interactions were compared among three phases-40-minute meditation (M), 5-minute Chakra-focusing practice (Z) and rest with closed eyes (R). The similarity index S, developed in nonlinear dynamical system theory, was employed to measure the degree of possibly asymmetric coupling. Meditators exhibited, overall, stronger interactions among multiple cortical areas in meditation stages M and Z than in the R state. This enhancement was greater in the M stage when the meditator was accompanied by a thought-free and fully consciousness state. In the high-frequency band (>13Hz), the interdependence was also higher in both meditation stages than at baseline rest. However, the interaction strength, especially in the posterior regions, was greatest in the Z stage, which involved internal attention. Few electrode pairs were observed with significant pair-wise asymmetry in the Z state. The similarity is a possible characteristic of dense reciprocal and strong mutual interactions between multiple cortical areas during meditation - especially in the Z state in the high-frequency band. These results demonstrate that profound Zen meditation induces various dynamic states in different phases of meditation, possibly reflected by nonlinear interdependence measure.