https://doi.org/10.1140/epjs/s11734-021-00413-5
Regular Article
Distribution of spiking and bursting in Rulkov’s neuron model
1
Instituto de Investigaciones Físicas, Campus Universitario Cota Cota, Universidad Mayor de San Andrés, La Paz, Bolivia
2
Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187, Dresden, Germany
3
Instituto de Altos Estudos da Paraíba, Rua Silvino Lopes 419-2502, 58039-190, João Pessoa, Brazil
4
Potsdam Institute for Climate Impact Research (PIK), 14473, Potsdam, Germany
5
Faculty of Water Science, Department of Water and Environmental Policy, University of Public Service, Ludovika tér 1, 1083, Budapest, Hungary
6
Complexity Sciences Center, 9225 Collins Avenue Suite 1208, 33154, Surfside, FL, USA
Received:
29
June
2021
Accepted:
16
December
2021
Published online:
5
January
2022
Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.
© The Author(s) 2022
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