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Title

Anticipation via canards in excitable systems

AuthorsKöksal Ersöz, Elif; Desroches, Mathieu; Mirasso, Claudio R. ; Rodrigues, Serafim
Issue Date2019
PublisherAmerican Institute of Physics
CitationChaos 29(1): 013111 (2019)
AbstractNeurons can anticipate incoming signals by exploiting a physiological mechanism that is not well understood. This article offers a novel explanation on how a receiver neuron can predict the sender's dynamics in a unidirectionally-coupled configuration, in which both sender and receiver follow the evolution of a multi-scale excitable system. We present a novel theoretical viewpoint based on a mathematical object, called canard, to explain anticipation in excitable systems. We provide a numerical approach, which allows to determine the transient effects of canards. To demonstrate the general validity of canard-mediated anticipation in the context of excitable systems, we illustrate our framework in two examples, a multi-scale radio-wave circuit (the van der Pol model) that inspired a caricature neuronal model (the FitzHugh-Nagumo model) and a biophysical neuronal model (a 2-dimensional reduction of the Hodgkin-Huxley model), where canards act as messengers to the senders' prediction. We also propose an experimental paradigm that would enable experimental neuroscientists to validate our predictions. We conclude with an outlook to possible fascinating research avenues to further unfold the mechanisms underpinning anticipation. We envisage that our approach can be employed by a wider class of excitable systems with appropriate theoretical extensions.
Publisher version (URL)http://doi.org/10.1063/1.5050018
URIhttp://hdl.handle.net/10261/204797
Identifiersdoi: 10.1063/1.5050018
issn: 1054-1500
e-issn: 1089-7682
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