Matrix analysis
A neural cocktail-party processor
Biological Cybernetics
Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Associative memory in a network of biological neurons
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Phase-coupling in two-dimensional networks of interacting oscillators
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Probability
Synchrony in excitatory neural networks
Neural Computation
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Evolution of Spiking Neural Controllers for Autonomous Vision-Based Robots
ER '01 Proceedings of the International Symposium on Evolutionary Robotics From Intelligent Robotics to Artificial Life
Emergent Neural Computational Architectures Based on Neuroscience - Towards Neuroscience-Inspired Computing
Populations of tightly coupled neurons: The rgc/lgn system
Neural Computation
Improved similarity measures for small sets of spike trains
Neural Computation
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Exploiting local stability, we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and, in the limit of a large number of interacting neighbors, also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem, we present a simple geometric method to verify the existence and local stability of a coherent oscillation.