Wave-separation in complex systems. Application to brain-signals

A departure from single-system dynamics, that may arise in characterizing self-organized dynamics of complex systems, is dealt with by using the Karhunen-Loève expansion of the trajectory matrix to decompose an experimental signal in a sum of spectral features. For an electroencephalographic α-signal, a separation of waves and extraction of additive sub-signals are achieved, each sub-signal covering a well-bounded and physiologically meaningful frequency range. From the subsignals, an attractor that vanishes on phase-randomizing the data is characterized, under conditions where none was found for the recorded signal.