Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Analysis of neural excitability and oscillations
Methods in neuronal modeling
Synchrony in excitatory neural networks
Neural Computation
The influence of limit cycle topology on the phase resetting curve
Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron
Neural Computation
A universal model for spike-frequency adaptation
Neural Computation
Computing and stability in cortical networks
Neural Computation
Computation of the Phase Response Curve: A Direct Numerical Approach
Neural Computation
Categorization of Neural Excitability Using Threshold Models
Neural Computation
The Combined Effects of Inhibitory and Electrical Synapses in Synchrony
Neural Computation
Minimal Models of Adapted Neuronal Response to In Vivo–lLike Input Currents
Neural Computation
Stationary Bumps in Networks of Spiking Neurons
Neural Computation
On Synchrony of Weakly Coupled Neurons at Low Firing Rate
Neural Computation
Synchrony in Heterogeneous Networks of Spiking Neurons
Neural Computation
Chaotic pattern transitions in pulse neural networks
Neural Networks
Event-driven simulations of nonlinear integrate-and-fire neurons
Neural Computation
Gamma oscillations and stimulus selection
Neural Computation
Neural Information Processing
Spike-timing error backpropagation in theta neuron networks
Neural Computation
Adaptive synchronization of activities in a recurrent network
Neural Computation
Study on the role of GABAergic synapses in synchronization
Neurocomputing
Bifurcations in Morris-Lecar neuron model
Neurocomputing
Synchronization transition in a pair of coupled non-identical oscillators
ICONIP'08 Proceedings of the 15th international conference on Advances in neuro-information processing - Volume Part I
2010 Special Issue: Bayesian estimation of phase response curves
Neural Networks
Convergence analysis of a numerical method to solve the adjoint linearized periodic orbit equations
Applied Numerical Mathematics
Model studies on time-scaled phase response curves and synchronization transition
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: theory and algorithms - Volume Part I
Synaptic and intrinsic determinants of the phase resetting curve for weak coupling
Journal of Computational Neuroscience
Phase-resetting curve determines how BK currents affect neuronal firing
Journal of Computational Neuroscience
Stability of two cluster solutions in pulse coupled networks of neural oscillators
Journal of Computational Neuroscience
A computational model of how cholinergic interneurons protect striatal-dependent learning
Journal of Cognitive Neuroscience
Thermal effects on phase response curves and synchronization transition
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Control of neural synchrony using channelrhodopsin-2: a computational study
Journal of Computational Neuroscience
Journal of Computational Neuroscience
Nonlinear dynamical analysis on coupled modified fitzhugh-nagumo neuron model
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Learning with single quadratic integrate-and-fire neuron
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Rewiring-induced chaos in pulse-coupled neural networks
Neural Computation
Detecting effective connectivity in networks of coupled neuronal oscillators
Journal of Computational Neuroscience
Journal of Computational Neuroscience
The neuron's modeling methods based on neurodynamics
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
FPGA-based biophysically-meaningful modeling of olivocerebellar neurons
Proceedings of the 2014 ACM/SIGDA international symposium on Field-programmable gate arrays
Synchronization of delayed coupled neurons in presence of inhomogeneity
Journal of Computational Neuroscience
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Type I membrane oscillators such as the Connor model (Connor et al. 1977) and the Morris-Lecar model (Morris and Lecar 1981) admit very low frequency oscillations near the critical applied current. Hansel et al. (1995) have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive. We use singular perturbation methods and averaging to show that this is a general property of Type I membrane models. We show in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation. We also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions.