Nonlinear dynamical systems describe neural activity at various scales and are frequently used to study brain functions and the impact of external perturbations. Here, we explore methods from optimal control theory (OCT) to study efficient, stimulating “control” signals designed to make the neural activity match desired targets. Efficiency is quantified by a cost functional, which trades control strength against closeness to the target activity. Pontryagin’s principle then enables to compute the cost-minimizing control signal. We then apply OCT to a Wilson–Cowan model of coupled excitatory and inhibitory neural populations. The model exhibits an oscillatory regime, low- and high-activity fixed points, and a bistable regime where low- and high-activity states coexist. We compute an optimal control for a state-switching (bistable regime) and a phase-shifting task (oscillatory regime) and allow for a finite transition period before penalizing the deviation from the target state. For the state-switching task, pulses of limited input strength push the activity minimally into the target basin of attraction. Pulse shapes do not change qualitatively when varying the duration of the transition period. For the phase-shifting task, periodic control signals cover the whole transition period. Amplitudes decrease when transition periods are extended, and their shapes are related to the phase sensitivity profile of the model to pulsed perturbations. Penalizing control strength via the integrated 1-norm yields control inputs targeting only one population for both tasks. Whether control inputs drive the excitatory or inhibitory population depends on the state-space location.
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Optimal control of a Wilson–Cowan model of neural population dynamics
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April 2023
Research Article|
April 19 2023
Optimal control of a Wilson–Cowan model of neural population dynamics
Special Collection:
Control of self-organizing nonlinear systems
Lena Salfenmoser
;
Lena Salfenmoser
a)
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing)
Institute of Software Engineering and Theoretical Computer Science, Technical University of Berlin
, 10623 Berlin, Germany
a)Author to whom correspondence should be addressed: lena.salfenmoser@tu-berlin.de
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Klaus Obermayer
Klaus Obermayer
b)
(Conceptualization, Formal analysis, Funding acquisition, Investigation, Supervision, Visualization, Writing – original draft, Writing – review & editing)
Institute of Software Engineering and Theoretical Computer Science, Technical University of Berlin
, 10623 Berlin, Germany
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a)Author to whom correspondence should be addressed: lena.salfenmoser@tu-berlin.de
b)
Also at: Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany.
Note: Control of self-organizing nonlinear systems.
Chaos 33, 043135 (2023)
Article history
Received:
January 31 2023
Accepted:
April 05 2023
Citation
Lena Salfenmoser, Klaus Obermayer; Optimal control of a Wilson–Cowan model of neural population dynamics. Chaos 1 April 2023; 33 (4): 043135. https://doi.org/10.1063/5.0144682
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