Abstract
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 language | English |
|---|---|
| Article number | 105103 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 83 |
| Early online date | 9 Nov 2019 |
| DOIs | |
| Publication status | E-pub ahead of print/First online - 9 Nov 2019 |
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Keywords
- Non-linear response
- Slow-fast analysis
- Cortical stimulation
- Neural mass model
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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. / Hebbink, Jurgen; van Gils, Stephan A.; Meijer, Hil Gaétan Ellart.
In: Communications in Nonlinear Science and Numerical Simulation, Vol. 83, 105103, 01.04.2020.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - On analysis of inputs triggering large nonlinear neural responses Slow-fast dynamics in the Wendling neural mass model
T2 - Slow-fast dynamics in the Wendling neural mass model
AU - Hebbink, Jurgen
AU - van Gils, Stephan A.
AU - Meijer, Hil Gaétan Ellart
PY - 2019/11/9
Y1 - 2019/11/9
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.
KW - Non-linear response
KW - Slow-fast analysis
KW - Cortical stimulation
KW - Neural mass model
UR - http://www.scopus.com/inward/record.url?scp=85074976983&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2019.105103
DO - 10.1016/j.cnsns.2019.105103
M3 - Article
VL - 83
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
M1 - 105103
ER -