2016/03/05 by Youngmin Park, Bard Ermentrout · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Neuroscience · Physics and Astronomy · Psychology · #Adiabatic process #Algorithm #Computer science #Coupling (piping) #Electrophysiology #Mathematics #Modulation (music) #Neural dynamics and brain function #Neuronal firing #Neuroscience #Nonlinear Dynamics and Pattern Formation #Perturbation (astronomy) #Physics #Psychology #Quantum mechanics #Statistical physics #Theory of computation #math.DS #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.1007/s10827-016-0596-6
28 pages, 11 figures
openalex publication_date 2016/03/05 · arxiv created 2016/03/08 · arxiv updated 2016/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Review Letters, 111, 214101, 2013) to include coupling. We apply the method to an all-to-all network and show that there is a waxing and waning of synchrony of modulated neurons.