Neuronal avalanches are a cortical phenomenon defined by bursts of neuronal firing encapsulated
by periods of quiescence. It has been found both in vivo and in vitro that neuronal avalanches
follow a power law distribution which is indicative of the system being within or near a critical
state. A system is critical if it is poised between order and disorder with the possibility of
minor event leading to a large chain reaction. This is also observed by the system exhibiting
a diverging correlation length between its components as it approaches the critical point. It
has been shown that neuronal criticality is a scale-free phenomenon observed throughout the
entire system as well as within each module of the system. At a small scale, neuronal networks
produce avalanches which conform to power law-like distributions. At a larger scale, we observe
that these systems consist of modules exhibiting long-range temporal correlations identifiable
via Detrended Fluctuation Analysis (DFA). This phenomenon is hypothesised to affect network
behaviour with regards to information processing, information storage, computational power, and
stability - The Criticality Hypothesis.
This thesis attempts to better understand critical neuronal networks and how criticality may
link with other neuronal phenomena. This work begins by investigating the interplay of network
connectivity, synaptic plasticity, and criticality. Using different network construction algorithms,
the thesis demonstrates that Hebbian learning and Spike Timing Dependent Plasticity (STDP)
robustly drive small networks towards a critical state. Moreover the thesis shows that, while
the initial distribution of synaptic weights plays a significant role in attaining criticality, the
network's topology at the modular level has little or no impact.
Using an expanded eight-module oscillatory spiking neural network the thesis then shows the
link between the different critical markers we use when attempting to observe critical behaviour
at different scales. The findings demonstrate that modules exhibiting power law-like behaviour
also demonstrate long-range temporal correlations throughout the system. Furthermore, we
show that when modules no longer exhibit power law-like behaviour we find that they become
uncorrelated or noisy. This shows a correlation between power law-like behaviour observed within
each module and the long-range temporal correlations between the modules.
The thesis concludes by demonstrating how criticality may be linked with other related phenomena,
namely metastability and dynamical complexity. Metastability is a global property of neuronal
populations that migrate between attractor-like states. Metastability can be quantified by the
variance of synchrony, a measure that has been hypothesised to capture the varying influence
neuronal populations have over one another and the system as a whole. The thesis shows
a correlation between critical behaviour and metastability where the latter is most reliably
maximised only when the former is near the critical state. This conclusion is expected as
metastability, similarly to criticality reflects the interplay between the integrating and segregating
tendencies of the system components. Agreeing with previous findings this suggests that
metastable dynamics may be another marker of critical behaviour.
A neural system is said to exhibit dynamical complexity if a balance of integrated and segregated
activity occurs within the system. A common attribute of critical systems is a balance between
excitation and inhibition. The final part of the thesis attempts to understand how criticality
may be linked with dynamical complexity. This work shows a possible connection between these
phenomena providing a foundation for further analysis. The thesis concludes with a discussion
of the significant role criticality plays in determining the behaviour of neuronal networks.