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Lotka–Volterra Like Dynamics in Phase Oscillator Networks

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Advances in Dynamics, Patterns, Cognition

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 20))

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Abstract

Many neural processes, including higher order cognitive functions, are characterized by metastable rather than attractor dynamics. Generalized Lotka–Volterra equations provide a suitable model that can give rise to switching dynamics between metastable equilibria and we review some results how such models can predict bounds on neural processing capacity. In this context generalized Lotka–Volterra system describes the interaction of macroscopic quantities rather than individual neural oscillators. We indicate a connection between generalized Lotka–Volterra equations and the mean field dynamics of networks of multiple identical populations of phase oscillators. This relationship not only gives insight into the global dynamics of phase oscillator populations but also hints at how spatiotemporal dynamics of synchronization can arise in phase oscillator networks.

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Acknowledgements

The author is indebted to M.I. Rabinovich for his guidance and support over the years. Moreover, he would like to thank P. Ashwin and E.A. Martens for many helpful discussions. This work has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007–2013) under REA grant agreement no. 626111.

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Authors and Affiliations

  1. Centre for Systems, Dynamics and Control and Department of Mathematics, University of Exeter, Exeter, EX4 4QF, UK

    Christian Bick

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  1. Christian Bick
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Correspondence to Christian Bick .

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Editors and Affiliations

  1. Pennsylvania State University, University Park, Pennsylvania, USA

    Igor S. Aranson

  2. Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany

    Arkady Pikovsky

  3. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Nikolai F. Rulkov

  4. BioCircuits Institute, University of California San Diego, La Jolla, California, USA

    Lev S. Tsimring

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Bick, C. (2017). Lotka–Volterra Like Dynamics in Phase Oscillator Networks. In: Aranson, I., Pikovsky, A., Rulkov, N., Tsimring, L. (eds) Advances in Dynamics, Patterns, Cognition. Nonlinear Systems and Complexity, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-53673-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-53673-6_8

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-53673-6

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