Name
Abstract | ||
|---|---|---|
Synchronization of neural oscillators has been well studied by both theorists and experimentalists. However, realistic details are often disregarded for tractability. Here, we consider a recurrent network of pulse-coupled neural oscillators since synaptic communication is often mediated by spikes. Neurons receive many stochastic inputs that have effects depending on the state of the neuron; thus, we incorporate phase-dependent (multiplicative) noise. Previous analysis of neural oscillators with additive noise (not necessarily weak) cannot be directly applied here because this results in analytically intractable equations that possibly have singularities. However, assuming weak coupling and weak noise, we accurately and analytically characterize various phenomena by a linear stability analysis around an asymptotic steady-state density approximation. Depending on the phase resetting curve, the system can undergo a supercritical Andronov-Hopf bifurcation as the recurrent coupling strength of the oscillator is increased, leading to synchronous and oscillatory population activity. The analysis is extended to include recurrent input through synapses with kinetics—it generally stabilizes the incoherent state. Moreover, input via synapses can uncover a bifurcation that does not exist with instantaneous recurrent input. The analysis is further generalized to recurrent input that is a smooth function of the population firing rate. The results are applied to a closed-loop system of neural oscillators that receive feedback mediated by a noisy population of excitable integrate-and-fire neurons. Our results extend the power of perturbation methods for dealing with equations that, a priori, appear intractable. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/090756065 | SIAM J. Applied Dynamical Systems |
Keywords | Field | DocType |
recurrent network,previous analysis,instantaneous recurrent input,neural oscillator,linear stability analysis,recurrent networks,stochastic input,pulse-coupled neural oscillator,pulse-coupled noisy neural oscillators,recurrent input,recurrent coupling strength,additive noise,steady state,multiplicative noise,kinetics,hopf bifurcation,oscillations | Population,Synchronization,Coupling,Multiplicative function,Control theory,A priori and a posteriori,Gravitational singularity,Mathematics,Multiplicative noise,Bifurcation | Journal |
Volume | Issue | ISSN |
3 | 1 | 1536-0040 |
Citations | PageRank | References |
3 | 0.39 | 17 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cheng Ly | 1 | 12 | 1.44 |
| G Bard Ermentrout | 2 | 292 | 123.65 |