Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics remains elusive. Here, we consider Wilson-Cowan networks and demonstrate through numerical and analytical work that homeostatic regulation of the network firing rates can paradoxically lead to a rich dynamical repertoire. The dynamics include mixed-mode oscillations, mixed-mode chaos, and chaotic synchronization when the homeostatic plasticity operates on a moderately slower time scale than the firing rates. This is true for a single recurrently coupled node, pairs of reciprocally coupled nodes without self-coupling, and networks coupled through experimentally determined weights derived from functional magnetic resonance imaging data. In all cases, the stability of the homeostatic set point is analytically determined or approximated. The dynamics at the network level are directly determined by the behavior of a single node system through synchronization in both oscillatory and non-oscillatory states. Our results demonstrate that rich dynamics can be preserved under homeostatic regulation or even be caused by homeostatic regulation.
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August 2018
Research Article|
August 24 2018
Chaos in homeostatically regulated neural systems
Wilten Nicola;
Wilten Nicola
a)
1
Department of Bioengineering, Imperial College London
, London SW7 2AZ, United Kingdom
a)Author to whom correspondence should be addressed: [email protected]
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Peter John Hellyer;
Peter John Hellyer
1
Department of Bioengineering, Imperial College London
, London SW7 2AZ, United Kingdom
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Sue Ann Campbell;
Sue Ann Campbell
2
Department of Applied Mathematics, University of Waterloo
, 200 University Avenue W., Waterloo, Ontario N2L 3G1, Canada
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Claudia Clopath
Claudia Clopath
1
Department of Bioengineering, Imperial College London
, London SW7 2AZ, United Kingdom
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a)Author to whom correspondence should be addressed: [email protected]
Chaos 28, 083104 (2018)
Article history
Received:
February 20 2018
Accepted:
July 09 2018
Citation
Wilten Nicola, Peter John Hellyer, Sue Ann Campbell, Claudia Clopath; Chaos in homeostatically regulated neural systems. Chaos 1 August 2018; 28 (8): 083104. https://doi.org/10.1063/1.5026489
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