Dynamical computation reservoir emerging within a biological model network

Abstract

Chaos in dynamical systems potentially provides many different dynamical states arising from a single attractor. We call this the reservoir property and give here a precise meaning to two aspects of such property. In both cases, the high flexibility of chaos comes into play, as compared to more regular regimes. In this article, we especially focus on the fact that chaotic attractors are known to possess an infinite number of embedded Unstable Periodic Orbits. In brain modeling, or for the purpose of suggesting computational devices that could take advantage of chaos, the different embedded dynamical states can be interpreted as different behaviors or computational modes suitable for particular tasks. Previously we proposed a rather abstract neural network model that mimicked cortex to some extent but where biological realism was not the major concern. In the present paper we show that the same potential for computation can be displayed by a more realistic neural model. The latter features spatiotemporal chaos of a type thus far only found in more "artificial" models. We also note that certain network-related properties, previously overlooked, turn out to be essential for the generation of complex behavior.

EEG Switching: Three Views from Dynamical Systems

“…As reported in [8], for these parameter values the system displays a form of low-dimensional spatiotemporal chaos. The dynamics is not periodic, but moderate coherence is observed in the neurons' activities.…”

“…This is the case for the parameter region considered [8]. Traveling waves are mathematically possible.…”

“…This parameter variation is part of a larger bifurcation path. A larger ω (2) range than the one shown here would produce a full period-doubling bifurcation scenario [8]. Figure 4 displays the EEG signal for ω (2) = 3.00 and ω (2) = 1.68, respectively.…”

“…One can observe multiple steady states, including global quiescence and global saturation, as well as a variety of oscillatory regimes for the electrical activity of the neurons. A form of spatiotemporal chaos is one of the observed complex regimes, as discussed in more detail in [8].…”

“…For lack of space in the present publication, we refer the reader to the detailed derivation of our model in [8]. Here we summarize only the main features.…”