By: Alexander V. Goltsev
From: Dep. Fisica, Univ. Aveiro
At: Complexo Interdisciplinar, Anfiteatro
Understanding the dynamics and structure of neuronal networks is a challenge for biologists, mathematicians and physicists. Neurons form complex nets of connections, where dendrites and axons extend, ramify, and form synaptic links between neurons. Due to long axons the structure of a typical neuronal network has small-world properties. Complex architectures of this kind are known to strongly influence processes taking place in networks. Apart from this highly heterogeneous structure, neural networks are noisy. Noise makes a stochastic approach to neuronal activities unavoidable. Intuitively, noise is damaging. However it has been observed in many neural systems that noise can play a positive role, supporting oscillations and synchrony between neurons or causing stochastic resonance. An investigation of these phenomena is of great importance for understanding of brain and cognitive function.
The present talk aims to give an introduction to small-world effect and architecture of complex networks. We discuss basic dynamical and structural properties of real neural networks, and a mechanism of interaction between neurons. A simple stochastic model based on ideas of cellular automata will be proposed for describing stochastic dynamics of neural networks. In the framework of an exact analytical approach and simulations, we will show the constructive role of noise in neural networks. In particular, global oscillations of neural populations and stochastic resonance are noise benefits in these strongly non-linear dynamical systems.