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Complex valued analyzing of cortical interactions play a major role in understanding of phase transitions (synchronizations) of the emergent cognitive dynamics of the brain, especially to obtain instantaneous local features in the frequency, phase and energyrepresentations. In the case of spatio-temporal signals in 64 channels, the analytic signal is computed by 1D Hilbert transform. Such 1D complex and hyper complex representations allow us to model brain coordination dynamics in the next step. The mathematical models can explain how neural populations at mesoscopic level interact together, engaging and disengaging from one population to another population. For those EcOG signals, the Riesz transform, partial and total Hilbert transforms and higher dimensional representations of signal for each waveform can also be formulated as processingfilter in the quaternion algebra. Geometric algeabric approaches are extensions of the 1D analytic signal which allow us to multiple operations on signals as low-/high-pass filter, n-order derivatives, local phase, local amplitude, localorientation of cortical interactions.Cortical interactions are defined in different types: multiple stable states, instability, state transitions, metastability. We implemented 64-channel intracranialmultichannel EEGsignals(EcOG) from rabbit which respond to conditioned stimuli. Those signals revealed emergent phase transitions associated with long range phase synchrony at some frame rates (episodes) in beta, alpha, delta, gamma and epsilon bands. We concluded that brain activity is wide spread synchronized with emergent amplitude and phase modulation (phase discontinuities) patterns. The patterns are based on relative local phase differences between local oscillations over time represented by each channel on a 8x8 grid structure. Finally we introduced a metric to understand the concept of global phase characteristics as phase synchrony index obtained by spatial analytic phase differences from 1D Hilbert transform.