Interactions of multiple rhythms in a biophysical network of neurons

Alexandros Gelastopoulos*, Nancy J. Kopell

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Neural oscillations, including rhythms in the beta1 band (12–20 Hz), are important in various cognitive functions. Often neural networks receive rhythmic input at frequencies different from their natural frequency, but very little is known about how such input affects the network’s behavior. We use a simplified, yet biophysical, model of a beta1 rhythm that occurs in the parietal cortex, in order to study its response to oscillatory inputs. We demonstrate that a cell has the ability to respond at the same time to two periodic stimuli of unrelated frequencies, firing in phase with one, but with a mean firing rate equal to that of the other. We show that this is a very general phenomenon, independent of the model used. We next show numerically that the behavior of a different cell, which is modeled as a high-dimensional dynamical system, can be described in a surprisingly simple way, owing to a reset that occurs in the state space when the cell fires. The interaction of the two cells leads to novel combinations of properties for neural dynamics, such as mode-locking to an input without phase-locking to it.

Original languageEnglish
Article number19
JournalJournal of Mathematical Neuroscience
Number of pages43
Publication statusPublished - 17. Nov 2020


  • Neural oscillations
  • Phase-locking
  • Phase-response curve
  • State reset
  • Time-division multiplexing

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