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Open AccessArticle

Birhythmic Analog Circuit Maze: A Nonlinear Neurostimulation Testbed

by Ian D. Jordan 1,2 and Il Memming Park 1,2,3,*
1
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA
2
Institute for Advanced Computing Science, Stony Brook University, Stony Brook, NY 11794, USA
3
Department of Neurobiology and Behavior, Stony Brook University, Stony Brook, NY 11794, USA
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(5), 537; https://doi.org/10.3390/e22050537
Received: 29 March 2020 / Revised: 4 May 2020 / Accepted: 9 May 2020 / Published: 11 May 2020
Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesized that some symptoms originate from the inability to spontaneously transition from one attractor to another. Using external perturbations, such as electrical pulses delivered by deep brain stimulation devices, it may be possible to induce such transition out of the pathological attractors. However, the induction of transition may be non-trivial, rendering the current open-loop stimulation strategies insufficient. In order to develop next-generation neural stimulators that can intelligently learn to induce attractor transitions, we require a platform to test the efficacy of such systems. To this end, we designed an analog circuit as a model for the multistable brain dynamics. The circuit spontaneously oscillates stably on two periods as an instantiation of a 3-dimensional continuous-time gated recurrent neural network. To discourage simple perturbation strategies, such as constant or random stimulation patterns from easily inducing transition between the stable limit cycles, we designed a state-dependent nonlinear circuit interface for external perturbation. We demonstrate the existence of nontrivial solutions to the transition problem in our circuit implementation. View Full-Text
Keywords: dynamical systems; bistability; birhythmic; analog circuit; neurostimulation dynamical systems; bistability; birhythmic; analog circuit; neurostimulation
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Jordan, I.D.; Park, I.M. Birhythmic Analog Circuit Maze: A Nonlinear Neurostimulation Testbed. Entropy 2020, 22, 537.

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