  As a promising computational paradigm, occurrence of critical states in
artificial and biological neural networks has attracted wide-spread attention.
An often-made explicit or implicit assumption is that one single critical state
is responsible for two separate notions of criticality (avalanche criticality
and dynamical edge of chaos criticality). Previously, we provided an isolated
counter-example for co-occurrence. Here, we reveal a persistent paradigm of
structural transitions that such networks undergo, as the overall connectivity
strength is varied over its biologically meaningful range. Among these
transitions, only one avalanche critical point emerges, with edge of chaos
failing to co-occur. Our observations are based on ensembles of networks
obtained from variations of network configuration and their neurons. This
suggests that not only non-coincidence of criticality, but also the persistent
paradigm of network structural changes in function of the overall connectivity
strength, could be generic features of a large class of biological neural
networks.

Neurons and Cognition;Chaotic Dynamics