Collective Dynamics in Neural Networks

Abstract

A wealth of natural and artificial systems are composed of many coupled subunits: examples are electric, metabolic, and neural networks that are encountered in engineering and biological contexts, but also the granular media and fluids studied in physics. In such cases, it is natural to expect substantial changes induced by the mutual coupling and it is customary to qualify the overall behaviour as collective. There exists, however, a deeper notion of the term collective, that is related to the concept of thermodynamic phase within equilibrium statistical mechanics. The same set of microscopic equations may generate and sustain different macroscopic states (see, e.g., the gas, liquid, and solid phases), that may be selected by varying a suitable control parameter (e.g., the temperature, or an external field). At equilibrium, the macroscopic phases are necessarily stationary (time-independent) but, out-of-equilibrium, detailed balance is violated, currents are generated and macroscopic oscillations may appear as well. The emergence of collective motion is particularly relevant in the context of neural networks, where its properties are likely to be connected to information processing in a way still to be understood.