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)