Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Alternating and synchronous rhythms in reciprocally inhibitory model neurons
Neural Computation
Reduction of conductance-based models with slow synapses to neural nets
Neural Computation
Synchrony in excitatory neural networks
Neural Computation
On numerical simulations of integrate-and-fire neural networks
Neural Computation
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Chaotic balanced state in a model of cortical circuits
Neural Computation
Patterns of Synchrony in Neural Networks with Spike Adaptation
Neural Computation
Synchrony in Heterogeneous Networks of Spiking Neurons
Neural Computation
Dynamics of Strongly Coupled Spiking Neurons
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron
Neural Computation
Hybrid integrate-and-fire model of a bursting neuron
Neural Computation
The Combined Effects of Inhibitory and Electrical Synapses in Synchrony
Neural Computation
Awaking and sleeping of a complex network
Neural Networks
Scaling effects in a model of the olfactory bulb
Neurocomputing
Stochastic dynamics of a finite-size spiking neural network
Neural Computation
Study on the role of GABAergic synapses in synchronization
Neurocomputing
Stability of two cluster solutions in pulse coupled networks of neural oscillators
Journal of Computational Neuroscience
Journal of Computational Neuroscience
Journal of Computational Neuroscience
Hi-index | 0.00 |
We investigate theoretically the conditions for the emergence of synchronous activity in large networks, consisting of two populations of extensively connected neurons, one excitatory and one inhibitory. The neurons are modeled with quadratic integrate-and-fire dynamics, which provide a very good approximation for the subthreshold behavior of a large class of neurons. In addition to their synaptic recurrent inputs, the neurons receive a tonic external input that varies from neuron to neuron. Because of its relative simplicity, this model can be studied analytically. We investigate the stability of the asynchronous state (AS) of the network with given average firing rates of the two populations. First, we show that the AS can remain stable even if the synaptic couplings are strong. Then we investigate the conditions under which this state can be destabilized. We show that this can happen in four generic ways. The first is a saddle-node bifurcation, which leads to another state with different average firing rates. This bifurcation, which occurs for strong enough recurrent excitation, does not correspond to the emergence of synchrony. In contrast, in the three other instability mechanisms, Hopf bifurcations, which correspond to the emergence of oscillatory synchronous activity, occur. We show that these mechanisms can be differentiated by the firing patterns they generate and their dependence on the mutual interactions of the inhibitory neurons and cross talk between the two populations. We also show that besides these codimension 1 bifurcations, the system can display several codimension 2 bifurcations: Takens-Bogdanov, Gavrielov-Guckenheimer, and double Hopf bifurcations.