Stochastic chaos versus deterministic chaos: a case for analog versus digital embodiment of devices for pattern recognition

摘要

Development of chaotic dynamics has been dominated by deterministic models that are stationary, autonomous, low-dimensional, and noise-free. Chaos in brains emerges from noisy synaptic interactions of immense numbers of neurons that stimulate and yet constrain each other, creating macroscopic order from microscopic disorder. Brains are nonstationary, unstable, constantly bombarded by sensory input, changing in functional dimension, and sustained by noise, yet they display a high degree of reliability and metastability in the proper conditions. Simulations of brain dynamics with digital models encounter the limits expressed in numerical instabilities imposed by finite approximations, attractor crowding, collapse into quasiperiodic solutions, the lack of shadowing trajectories, and the curse of "infinite sensitivity to the initial conditions"Analog embodiments may take advantage of the use of continuous variables, highly parallel integrative operations, and reliance on internally generated noise that is not only unavoidable but essential for normal function. The major unsolved problem in applying the theory of stochastic chaos is generating, controlling and measuring global chaotic attractors with multiple wings.