Nonlinear Interdependence (S) Measures used for Exploring Chaotic Behavior in Large-Scale Neuro-Models

As the theory of nonlinear dynamics clearly shows, a state space is the natural framework in which the properties of nonlinear dynamical systems can be described and quantified. These properties may be undetectable in the time domain of the system output, e.g., in the EEG tracing. Nonlinear Interdependence, (S), proposed by Quiroga, is said to occur when the trajectories reconstructed in the phase-space of one time series, experimentally predict the evolution of the phase space trajectories of the second time series. A phase space representation may reveal the salient features of the nonlinear structure which are hidden or occluded to standard linear approaches. This measure of predictability has the advantage over linear measures, of being sensitive to interdependence between dissimilar types of activity. In this paper we present a comparison between a nonlinear measure (the Nonlinear Interdependence, S) and a linear measure (the Cross Correlation coefficient, CC). In many cases where one analyzes nonlinear signals, CC is a measures that well describes the synchronization or the desynchronization between two signals. In other cases, S is introduced in addition to CC in order to describe the nonlinear signals. This paper investigates a biologically-realistic neural network (NN) model of the piriform cortex. Our previous work studied the EEGs obtained from two components of this network. In this current work, we increase the granularity of our approach and replicate the exploration using the membrane potentials of our neurons. We thus investigate here the synchronization of these types of signals using the membrane potentials using both linear measures (i.e., CC) and nonlinear measures (i.e., S). Our results clearly prove that utilizing both these measures is effective in analyzing and understanding real-life chaotic systems