Neuronal avalanches in complex networks

Abstract

Brain networks are neither regular nor random. Their structure allows for optimal information processing and transmission across the entire neural substrate of an organism. However, for topological features to be appropriately harnessed, brain networks should implement a dynamical regime which prevents phase-locked and chaotic behaviour. Critical neural dynamics refer to a dynamical regime in which the system is poised at the boundary between regularity and randomness. It has been reported that neural systems poised at this boundary achieve maximum computational power. In this paper, we review recent results regarding critical neural dynamics that emerge from systems whose underlying structure exhibits complex network properties.

Keywords:

• neuronal avalanches
• self-organised criticality
• complex networks
• phase transitions
• scale-free networks
• small-world networks
• complex collective dynamics of the brain

PACS numbers:

• 05.65.+b
• 05.70.Fh
• 05.70.Jk

Public Interest Statement

It is not merely the sheer amount of nerve cells and synaptic connections between them that is responsible for the immense capabilities of a brain. More important are the intricate patterns of connectivity which are unlikely to be specified in detail by genetic or environmental information. We study effects of such connectivity patterns on the activity dynamics and consider in particular the phenomenon of criticality which refers to the brain's ability to remain flexible and responsive for a large diversity of sensory inputs. While we and other authors have proposed a number of mechanisms how a brain can manage a critical state, the role of the specific connection patterns is less well understood. Here, we discuss several classes of network structures and show how they enhance critical behaviour in the brain. It remains an interesting question whether these structures are the cause or the consequence of a critical dynamics.

Additional information

Funding

Funding. The authors received no direct funding for this research.

Notes on contributors

Victor Hernandez-Urbina

Victor Hernandez-Urbina completed his PhD in Neuroinformatics at the University of Edinburgh. He studied criticality in neural systems, complex networks and synaptic plasticity under the supervision of Michael Herrmann. 

J. Michael Herrmann

Having received a Doctorate from the University of Leipzig in 1993, J. Michael Herrmann continues to work on computational neuroscience and theoretical aspects of artificial neural networks. He has contributed to establish the concept of criticality in these fields and has been active to apply approaches related to criticality also in the emerging field of neurorobotics. As a Lecturer for Robotics at the School of Informatics, University of Edinburgh, his research interests include also self-organisation, robot learning, neural avalanches, auditory system, bio-medical data analysis, metaheuristic optimisation and information theory.