On analysis of inputs triggering large nonlinear neural responses Slow-fast dynamics in the Wendling neural mass model: Slow-fast dynamics in the Wendling neural mass model

Jurgen Hebbink*, Stephan A. van Gils, Hil Gaétan Ellart Meijer

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    Many applications in neuroscience, such as electrical and magnetic stimulation, can be modelled as short transient input to non-linear dynamical systems. In excitable systems, small input yields more or less linear responses, while for increasing stimulation strength large non-linear responses may show up suddenly. A challenging task is to determine the transition between the two different response types.

    In this work we consider such a transition between normal and pathological responses in a model of coupled Wendling neural masses as we encountered in a previous study. First, the different timescales of inhibition in this model allow a slow-fast analysis. This reveals two different dynamical regimes for the systems’ response. Second, the two response types are separated by a high-dimensional stable manifold of a saddle slow manifold. Large pathological responses appear if the fast subsystem escapes from this manifold to another attractor. The typical fast oscillations seen during the pathological responses are explained by the bifurcation diagram of the fast subsystem. Under normal conditions these oscillations are suppressed by slow inhibition. External stimulation temporarily releases the fast subsystem from this slow inhibition. The critical response can be formulated as a boundary value problem with one free parameter and can be used to study the dependency of the transition between the two response types upon the system parameters.
    Original languageEnglish
    Article number105103
    JournalCommunications in Nonlinear Science and Numerical Simulation
    Volume83
    Early online date9 Nov 2019
    DOIs
    Publication statusE-pub ahead of print/First online - 9 Nov 2019

    Fingerprint

    Nonlinear dynamical systems
    Boundary value problems
    Subsystem
    Model
    Oscillation
    Slow Manifold
    Excitable Systems
    Stable Manifold
    Neuroscience
    Nonlinear Response
    Linear Response
    Nonlinear Dynamical Systems
    Saddle
    Bifurcation Diagram
    Attractor
    Time Scales
    High-dimensional
    Boundary Value Problem

    Keywords

    • Non-linear response
    • Slow-fast analysis
    • Cortical stimulation
    • Neural mass model

    Cite this

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    title = "On analysis of inputs triggering large nonlinear neural responses Slow-fast dynamics in the Wendling neural mass model: Slow-fast dynamics in the Wendling neural mass model",
    abstract = "Many applications in neuroscience, such as electrical and magnetic stimulation, can be modelled as short transient input to non-linear dynamical systems. In excitable systems, small input yields more or less linear responses, while for increasing stimulation strength large non-linear responses may show up suddenly. A challenging task is to determine the transition between the two different response types.In this work we consider such a transition between normal and pathological responses in a model of coupled Wendling neural masses as we encountered in a previous study. First, the different timescales of inhibition in this model allow a slow-fast analysis. This reveals two different dynamical regimes for the systems’ response. Second, the two response types are separated by a high-dimensional stable manifold of a saddle slow manifold. Large pathological responses appear if the fast subsystem escapes from this manifold to another attractor. The typical fast oscillations seen during the pathological responses are explained by the bifurcation diagram of the fast subsystem. Under normal conditions these oscillations are suppressed by slow inhibition. External stimulation temporarily releases the fast subsystem from this slow inhibition. The critical response can be formulated as a boundary value problem with one free parameter and can be used to study the dependency of the transition between the two response types upon the system parameters.",
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    author = "Jurgen Hebbink and {van Gils}, {Stephan A.} and Meijer, {Hil Ga{\'e}tan Ellart}",
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    AU - Meijer, Hil Gaétan Ellart

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    N2 - Many applications in neuroscience, such as electrical and magnetic stimulation, can be modelled as short transient input to non-linear dynamical systems. In excitable systems, small input yields more or less linear responses, while for increasing stimulation strength large non-linear responses may show up suddenly. A challenging task is to determine the transition between the two different response types.In this work we consider such a transition between normal and pathological responses in a model of coupled Wendling neural masses as we encountered in a previous study. First, the different timescales of inhibition in this model allow a slow-fast analysis. This reveals two different dynamical regimes for the systems’ response. Second, the two response types are separated by a high-dimensional stable manifold of a saddle slow manifold. Large pathological responses appear if the fast subsystem escapes from this manifold to another attractor. The typical fast oscillations seen during the pathological responses are explained by the bifurcation diagram of the fast subsystem. Under normal conditions these oscillations are suppressed by slow inhibition. External stimulation temporarily releases the fast subsystem from this slow inhibition. The critical response can be formulated as a boundary value problem with one free parameter and can be used to study the dependency of the transition between the two response types upon the system parameters.

    AB - Many applications in neuroscience, such as electrical and magnetic stimulation, can be modelled as short transient input to non-linear dynamical systems. In excitable systems, small input yields more or less linear responses, while for increasing stimulation strength large non-linear responses may show up suddenly. A challenging task is to determine the transition between the two different response types.In this work we consider such a transition between normal and pathological responses in a model of coupled Wendling neural masses as we encountered in a previous study. First, the different timescales of inhibition in this model allow a slow-fast analysis. This reveals two different dynamical regimes for the systems’ response. Second, the two response types are separated by a high-dimensional stable manifold of a saddle slow manifold. Large pathological responses appear if the fast subsystem escapes from this manifold to another attractor. The typical fast oscillations seen during the pathological responses are explained by the bifurcation diagram of the fast subsystem. Under normal conditions these oscillations are suppressed by slow inhibition. External stimulation temporarily releases the fast subsystem from this slow inhibition. The critical response can be formulated as a boundary value problem with one free parameter and can be used to study the dependency of the transition between the two response types upon the system parameters.

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