It has been proposed that criticality, defined as the border zone between two phases (or different collective states) in which self-organizing systems, both physical and biological, can be found, corresponds to a dynamic equilibrium in these systems.  This can be interpreted, in the biological case, as the natural state to which evolving systems tend, so that they optimize the antagonistic requirements of robustness and adaptability.  This has been verified, for example, through accurate measurement of heart rate variability at rest in young, healthy mammals, including humans.  The mathematical definition has to do with the scale invariance in the power spectrum of the measured signal.  However, in the case of systems that emit multiple signals (i.e. multivariables), such as those corresponding to a brain EEG or to the measurement of multiple individual neurons, the traditional definition relies on the way in which these systems respond to external stimuli.  In this talk I present a new definition of criticality in multivariable systems
and I show its validity in an extension of the Ising model, a classic criticality laboratory.  I also present some preliminary results for the case of EEG's.

1) Center for Complexity Sciences, Unam, 2) Institute of Nuclear Sciences, Unam, 3) El Colegio Nacional