Convergent activation dynamics in continuous time networks
Neural Networks
Oscillations and synchronization in neural networks: an exploration of the labeling
International Journal of Neural Systems
Metastable bubble solutions for the Allen-Cahn equation with mass conservation
SIAM Journal on Applied Mathematics
Exponential transients in continuous-time Liapunov systems
Theoretical Computer Science
Desynchronized stable states in diluted neural networks
Neurocomputing
How delays affect neural dynamics and learning
IEEE Transactions on Neural Networks
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We study the propagation of pulse sequences in a chain of neurons with sigmoidal input-output relations. The propagating speeds of pulse fronts depend on the widths of the preceding pulses and adjacent pulse fronts interact attractively. Sequences of pulse widths are then modulated through transmission. Equations for changes in pulse width sequences are derived with a kinematical model of propagating pulse fronts. The transmission of pulse width sequences in the chain is expressed as a linear system with additive noise. The gain of the system function increases exponentially with the number of neurons in a high-frequency region. The power spectrum of variations in pulse widths due to spatiotemporal noise also increases in the same manner. Further, the interaction between pulse fronts keeps the coherence and mutual information of initial and transmitted pulse sequences. Results of an experiment on an analog circuit confirm these properties.