On the Phase Reduction and Response Dynamics of Neural Oscillator Populations

By E. Shea-Brown, Jeff Moehlis, Philip J. Holmes. Neural Computation, 2004

548 citations recorded by the source corpus.

Subfields: Cellular and Molecular Neuroscience, Cognitive Neuroscience, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f1998fc20012ca14d22aac2f0497e5b493a12290

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cellular and Molecular Neuroscience

1. Xiao-Jing Wang
2. Francesco Bullo
3. Florian Dörfler
4. Avik De
5. Hiroya Nakao
6. Eugene M. Izhikevich
7. Philip J. Holmes
8. Gustavo Deco

In Cognitive Neuroscience

1. Francesco Bullo
2. Florian Dörfler
3. Xiao-Jing Wang
4. Derek A. Paley
5. Philip J. Holmes
6. Rodolphe Sepulchre
7. Naomi Ehrich Leonard
8. Avik De

In Statistical and Nonlinear Physics

1. Xiao-Jing Wang
2. Philip J. Holmes
3. Hiroya Nakao
4. Avik De
5. Francesco Bullo
6. Florian Dörfler
7. John M. Guckenheimer
8. Aneta Stefanovska

Citations in the corpus

• Modular Hopping and Running via Parallel Composition (2017, methodology): “Phase response curves (PRC’s) Brown et al. (2004) are used in the study of neural circuits; they describe the phase response of the oscillator to perturbations in various states that couple into the phase dynamics.”
• Stabilization of Planar Collective Motion: All-to-All Communication (2007, background): “This all-to-all sinusoidal coupling (5) is the most frequently studied coupling in the literature of coupled oscillators [11], [19], [ 24 ].”
• Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (2006, background): “(Brown et al. 2004) Show that PRC for an oscillator near saddle homoclinic orbit bifurcation scales as PRC (θ) ∼ eλ(T−θ), where λ is the positive eigenvalue of the saddle and T is the period of oscillation.”
• Stabilization of Planar Collective Motion With Limited Communication (2008, background): “The all-to-all sinusoidal coupling (5) with m =1 is a frequently studied coupling in the literature of coupled oscillators [28]‐[ 30 ].”
• Generative Models of Cortical Oscillations: Neurobiological Implications of the Kuramoto Model (2010, unknown): “This phase reduction approach has now become a standard technique in computational neurosciences (see, e.g., Ermentrout and Kopell, 1986, 1990; Guckenheimer and Holmes, 1990; Tass, 1999; Brown et al., 2004).”
• Coupling functions:universal insights into dynamical interaction mechanisms (2017, background): “…oscillators subject to noise of different kinds, for oscillating neuronal populations, and for spatiotemporal oscillations in reactiondiffusion systems (Brown et al., 2004; Goldobin et al., 2010; Kurebayashi et al., 2013; Nakao et al., 2014; Teramae et al., 2009; Yoshimura and Arai, 2008).”
• Neurophysiological and Computational Principles of Cortical Rhythms in Cognition (2010, methodology): “Unlike the classic Hodgkin-Huxley model, a neuronal PRC may not display a significant “negative lobe” (119, 275, 658).”
• Phase reduction approach to synchronisation of nonlinear oscillators (2016, methodology): “We here derive the adjoint equation, based on the simple argument by Brown, Moehlis, and Holmes [29].”
• Synchronization in complex networks of phase oscillators: A survey (2014, methodology): “Hence, the iPRC serves as a natural analysis (Sacré and Sepulchre, 2014; Sacré, 2013; Brown et al., 2004) and design (Wang et al., 2013; Wang and Doyle, 2012) tool for general limit-cycle oscillator networks.”
• The Dynamics of Legged Locomotion: Models, Analyses, and Challenges (2006, methodology): “In this section we introduce models at two different levels that address the rhythm generation, coordination, and control behaviors to be reviewed in section 2.4 and taken up again in greater technical detail in section 5.”