Generative Models of Cortical Oscillations: Neurobiological Implications of the Kuramoto Model

By Michael Breakspear, Stewart Heitmann, Andreas Daffertshofer. Frontiers in Human Neuroscience, 2010

513 citations recorded by the source corpus.

Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, and which has elucidated the core mechanisms of a range of biological and physical phenomena. In this paper, we provide a brief introduction to the Kuramoto model in its original, rather abstract, form and then focus on modifications that increase its neurobiological plausibility by incorporating topological properties of local cortical connectivity. The extended model elicits elaborate spatial patterns of synchronous oscillations that exhibit persistent dynamical instabilities reminiscent of cortical activity. We review how the Kuramoto model may be recast from an ordinary differential equation to a population level description using the nonlinear Fokker–Planck equation. We argue that such formulations are able to provide a mechanistic and unifying explanation of oscillatory phenomena in the human cortex, such as fluctuating beta oscillations, and their relationship to basic computational processes including multistability, criticality, and information capacity.

Subfields: Cognitive Neuroscience, Computer Networks and Communications, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/72a5145ee8b2de8061b308cde13f159d537eb9c1

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Citations in the corpus

The Kuramoto model in complex networks (2015, background): “On the other hand, in some situations, the models can be simplified to coupled phase oscillators akin to the Kuramoto model, which still yields a rich and non-trivial dynamics while being neurobiologically plausible [377].”
A Free Energy Principle for Biological Systems (2012, background): “The same theme of circular causality is seen in nonlinear Fokker-Planck formulations of coupled nonlinear random dynamical systems [48,49], where (macroscopic) mean field effects couple back to the density over (microscopic) states by changing their flow.”
A free energy principle for a particular physics (2019, background): “n et al., 2013), which – to an empirical eye – will manifest as oscillations. This is interesting because much of empirical neuroscience (and beyond) is occupied with oscillations and their ontology (Breakspear et al., 2010; Burgess et al., 2007; Buzsaki, 1998; Buzsaki and Moser, 2013; Giraud and Po”
Coupling functions:universal insights into dynamical interaction mechanisms (2017, methodology): “Today this model is the cornerstone for many studies and applications (Acebrón et al., 2005; Strogatz, 2000), including neuroscience (Breakspear et al., 2010; Cabral et al., 2014; Cumin and Unsworth, 2007), Josephsonjunction arrays (Filatrella et al., 2000; Wiesenfeld et al., 1996, 1998), power…”
Exploring mechanisms of spontaneous functional connectivity in MEG: How delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations (2014, unknown): “, 2001; Strogatz, 2003) and, more recently, neural dynamics (Breakspear et al., 2010; Cabral et al., 2011; Kitzbichler et al., 2009; Yan and Li, 2013).”