Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons
Abstract
We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we generalize our results to directed trees of model neurons with heterogeneous inputs.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 01, 2019
- Source ID
- 10.1063/1.5050178
Entities
People
- Biswadip Dey
- Elizabeth N. Davison
- Naomi Ehrich Leonard
- Zahra Aminzare
Organizations
- National Science Foundation
- Office of Naval Research
- Princeton University
- University of Iowa