Co-evolutionary dynamics for two adaptively coupled Theta neurons
Augustsson, Felix LU
and Martens, Erik A.
LU
(2024)
In Chaos
34(11).
- Abstract
Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is crucial for deciphering a range of phenomena from brain activity to power grid stability. Recent interest in co-evolutionary networks has highlighted the intricate interplay between dynamics on and of the network with mixed time scales. Here, we explore the collective behavior of excitable oscillators in a simple network of two Theta neurons with adaptive coupling without self-interaction. Through a combination of bifurcation analysis and numerical simulations, we seek to understand how the level of... (More)
Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is crucial for deciphering a range of phenomena from brain activity to power grid stability. Recent interest in co-evolutionary networks has highlighted the intricate interplay between dynamics on and of the network with mixed time scales. Here, we explore the collective behavior of excitable oscillators in a simple network of two Theta neurons with adaptive coupling without self-interaction. Through a combination of bifurcation analysis and numerical simulations, we seek to understand how the level of adaptivity in the coupling strength, a , influences the dynamics. We first investigate the dynamics possible in the non-adaptive limit; our bifurcation analysis reveals stability regions of quiescence and spiking behaviors, where the spiking frequencies mode-lock in a variety of configurations. Second, as we increase the adaptivity a , we observe a widening of the associated Arnol’d tongues, which may overlap and give room for multi-stable configurations. For larger adaptivity, the mode-locked regions may further undergo a period-doubling cascade into chaos. Our findings contribute to the mathematical theory of adaptive networks and offer insights into the potential mechanisms underlying neuronal communication and synchronization.
(Less)
- author
- Augustsson, Felix
LU
and Martens, Erik A.
LU
- organization
- publishing date
- 2024-11-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Coupled oscillators, Phase space methods, Neuron model
- in
- Chaos
- volume
- 34
- issue
- 11
- article number
- 113126
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- scopus:85209400824
- pmid:39541264
- ISSN
- 1054-1500
- DOI
- 10.1063/5.0226338
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2024 Author(s).
- id
- 327e0c58-c3b9-42dd-bf24-06d6614b9a93
- date added to LUP
- 2024-12-01 15:30:57
- date last changed
- 2025-07-14 09:22:35
@article{327e0c58-c3b9-42dd-bf24-06d6614b9a93,
abstract = {{<p>Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is crucial for deciphering a range of phenomena from brain activity to power grid stability. Recent interest in co-evolutionary networks has highlighted the intricate interplay between dynamics on and of the network with mixed time scales. Here, we explore the collective behavior of excitable oscillators in a simple network of two Theta neurons with adaptive coupling without self-interaction. Through a combination of bifurcation analysis and numerical simulations, we seek to understand how the level of adaptivity in the coupling strength, a , influences the dynamics. We first investigate the dynamics possible in the non-adaptive limit; our bifurcation analysis reveals stability regions of quiescence and spiking behaviors, where the spiking frequencies mode-lock in a variety of configurations. Second, as we increase the adaptivity a , we observe a widening of the associated Arnol’d tongues, which may overlap and give room for multi-stable configurations. For larger adaptivity, the mode-locked regions may further undergo a period-doubling cascade into chaos. Our findings contribute to the mathematical theory of adaptive networks and offer insights into the potential mechanisms underlying neuronal communication and synchronization.</p>}},
author = {{Augustsson, Felix and Martens, Erik A.}},
issn = {{1054-1500}},
keywords = {{Coupled oscillators; Phase space methods; Neuron model}},
language = {{eng}},
month = {{11}},
number = {{11}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Chaos}},
title = {{Co-evolutionary dynamics for two adaptively coupled Theta neurons}},
url = {{http://dx.doi.org/10.1063/5.0226338}},
doi = {{10.1063/5.0226338}},
volume = {{34}},
year = {{2024}},
}