A stochastic theory of phase transitions in human hand movement
Biological Cybernetics
The slow passage through a Hopf bifurcation: delay, memory effects, and resonance
SIAM Journal on Applied Mathematics
Learning of phase lags in coupled neural oscillators
Neural Computation
On-off intermittency: power spectrum and fractal properties of time series
MSTD '95 Proceedings of the workshop on Measures of spatio-temporal dynamics
The handbook of brain theory and neural networks
Spiral Waves in Integrate-and-Fire Neural Networks
Advances in Neural Information Processing Systems 5, [NIPS Conference]
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Rapid advances in technology are making the dream of treating human neurological diseases with implanted electronic devices a reality. The more such devices are able to exploit the properties of intrinsic neural control mechanisms, the more effective they will be in re-establishing control in the setting of disease. Noise and time delays are ubiquitous features of the nervous system. Three observations suggest that in order to understand control in noisy neural dynamical systems with retarded variables it will be necessary to change the focus from the identification and characterization of attractors to a study of phenomena that occur near stability boundaries (i.e., "critical phenomena"): 1) multistability has been identified in simple neural loops, the onset of epileptic seizures, and human postural sway; 2) on-off intermittency and 3) power laws arise in the nervous system. These observations support the possibility of developing strategies that treat neurological disease by the addition of appropriately designed stimuli, including noise.