June 28, 2007
Although neurons as computational elements are 7 orders of magnitude slower than their artificial counterparts, the primate brain grossly outperforms robotic algorithms in all but the most structured tasks. Parallelism alone is a poor explanation, and much recent functional modelling of the central nervous system focuses on its modular, heavily feedback-based computational architecture, the result of accumulation of subsystems throughout evolution.
We discuss this architecture from a global stability and convergence point of view. We then study synchronization as a model of computations at different scales in the brain, such as pattern matching, segmentation, temporal binding of sensory data, and mirror neuron response.
Finally, we derive a simple condition for a general dynamical system to globally converge to a regime where multiple groups of fully synchronized elements coexist. Applications of such « polyrhythms » to some classical questions in robotics and systems neuroscience are discussed.
The development makes extensive use of nonlinear contraction theory, a comparatively recent analysis tool whose main features will be briefly reviewed.
Jean-Jacques Slotine (MIT, USA)