Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Relative phase behavior of two slowly coupled oscillators
SIAM Journal on Applied Mathematics
Reduction of conductance-based models with slow synapses to neural nets
Neural Computation
Synchrony in excitatory neural networks
Neural Computation
Weakly connected neural networks
Weakly connected neural networks
Linearization of F-1 curves by adaptation
Neural Computation
A dynamical theory of spike train transitions in networks of integrate-and-fire oscillators
SIAM Journal on Applied Mathematics
Simulating, Analyzing, and Animating Dynamical Systems: A Guide Toi Xppaut for Researchers and Students
Neuronal Networks of the Hippocampus
Neuronal Networks of the Hippocampus
Stationary Bumps in Networks of Spiking Neurons
Neural Computation
Patterns of Synchrony in Neural Networks with Spike Adaptation
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
IEEE Transactions on Neural Networks
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Synapses that rise quickly but have long persistence are shown to have certain computational advantages. They have some unique mathematical properties as well and in some instances can make neurons behave as if they are weakly coupled oscillators. This property allows us to determine their synchronization properties. Furthermore, slowly decaying synapses allow recurrent networks to maintain excitation in the absence of inputs, whereas faster decaying synapses do not. There is an interaction between the synaptic strength and the persistence that allows recurrent networks to fire at low rates if the synapses are sufficiently slow. Waves and localized structures are constructed in spatially extended networks with slowly decaying synapses.