Neuronal networks and controlled symmetries, a generic framework

The extraordinary computational power of the brain may be related in part to the fact that each of the smaller neural networks that compose it can behave transiently in many different ways, depending on its inputs. Mathematically, input continuity helps to show how a large network, constructed recursively from smaller blocks, can exhibit robust specific properties according to its input. By extending earlier work on synchrony and symmetry, we exploit input continuity of contracting systems to ensure robust control of diverse spatial and spatio-temporal symmetries of the output signal in such a network.