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

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      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.

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            Author and article information

            1simpleSchool of Psychiatry, University of New South Wales Sydney, NSW, Australia
            2simpleThe Black Dog Institute, Prince of Wales Hospital Sydney, NSW, Australia
            3simpleQueensland Institute of Medical Research Brisbane, QLD, Australia
            4simpleRoyal Brisbane and Women's Hospital, Brisbane QLD, Australia
            5simpleResearch Institute MOVE, VU University Amsterdam Amsterdam, Netherlands
            Author notes

            Edited by: Kai J. Miller, University of Washington, USA

            Reviewed by: Carson Chow, University of Pittsburgh, USA; National Institutes of Health, USA; Ole Paulsen, University of Cambridge, UK; University of Oxford, UK

            *Correspondence: Michael Breakspear, 300 Herston Rd, Herston, QLD, 4009, Australia.; e-mail: mbreak@
            Front Hum Neurosci
            Front. Hum. Neurosci.
            Frontiers in Human Neuroscience
            Frontiers Research Foundation
            11 November 2010
            : 4
            Copyright © 2010 Breakspear, Heitmann and Daffertshofer.

            This is an open-access article subject to an exclusive license agreement between the authors and the Frontiers Research Foundation, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are credited.

            Figures: 6, Tables: 0, Equations: 27, References: 86, Pages: 14, Words: 10919
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