Dynamical origin of complex motor patterns (Vol. 41, No. 6)
Many motor patterns in biology are surprisingly simple, particularly taking into account that they are generated by complex neural networks. During song, for example, some songbirds have to generate periodic fluctuations in their air sac pressure and syringeal muscle tension in order to achieve sounds with the adequate acoustic properties. For the case of domestic canaries, the different respiratory patterns used during song were found to be sub-harmonic solutions of a simple, low dimensional dynamical system. Yet, these gestures are generated by thousands of neurons operating in a non-synchronous regime. How can the average activity present the precise, non-trivial features of the solutions of a low dimensional nonlinear dynamical system?
Inspired by this example, we address the general issue of the emergence of low dimensional, non-trivial dynamics out of large, complex interacting units.
In the spirit of classical statistical mechanics, the equations obeyed by the order parameter of a population of globally coupled nonlinear units are derived. The analysis allows showing that non-trivial yet low-dimensional dynamics is possible in average, even in a non-synchronic regime, providing a new mechanism for dimensionality reduction in the dynamics of complex systems.