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

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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

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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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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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