Wave Generation in Unidirectional Chains of Idealized Neural Oscillators View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-12

AUTHORS

Bastien Fernandez, Stanislav M. Mintchev

ABSTRACT

We investigate the dynamics of unidirectional semi-infinite chains of type-I oscillators that are periodically forced at their root node, as an archetype of wave generation in neural networks. In previous studies, numerical simulations based on uniform forcing have revealed that trajectories approach a traveling wave in the far-downstream, large time limit. While this phenomenon seems typical, it is hardly anticipated because the system does not exhibit any of the crucial properties employed in available proofs of existence of traveling waves in lattice dynamical systems. Here, we give a full mathematical proof of generation under uniform forcing in a simple piecewise affine setting for which the dynamics can be solved explicitly. In particular, our analysis proves existence, global stability, and robustness with respect to perturbations of the forcing, of families of waves with arbitrary period/wave number in some range, for every value of the parameters in the system. More... »

PAGES

5

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13408-016-0037-x

DOI

http://dx.doi.org/10.1186/s13408-016-0037-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1044762465

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/27059027


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