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Hutt A, Rich S, Valiante TA, Lefebvre J. Intrinsic neural diversity quenches the dynamic volatility of neural networks. Proc Natl Acad Sci U S A 2023; 120:e2218841120. [PMID: 37399421 PMCID: PMC10334753 DOI: 10.1073/pnas.2218841120] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 05/19/2023] [Indexed: 07/05/2023] Open
Abstract
Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical diversity enriches neural systems' dynamical repertoire, it remains challenging to reconcile with the robustness and persistence of brain function over time (resilience). To better understand the relationship between excitability heterogeneity (variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations-signs of instability-in response to a slowly varying modulatory fluctuation. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell heterogeneity in the robustness of brain function in the face of change.
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Affiliation(s)
- Axel Hutt
- Université de Strasbourg, CNRS, Inria, ICube, MLMS, MIMESIS, StrasbourgF-67000, France
| | - Scott Rich
- Krembil Brain Institute, Division of Clinical and Computational Neuroscience, University Health Network, Toronto, ONM5T 0S8, Canada
| | - Taufik A. Valiante
- Krembil Brain Institute, Division of Clinical and Computational Neuroscience, University Health Network, Toronto, ONM5T 0S8, Canada
- Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONM5S 3G8, Canada
- Institute of Biomedical Engineering, University of Toronto, Toronto, ONM5S 3G9, Canada
- Institute of Medical Sciences, University of Toronto, Toronto, ONM5S 1A8, Canada
- Division of Neurosurgery, Department of Surgery, University of Toronto, Toronto, ONM5G 2C4, Canada
- Center for Advancing Neurotechnological Innovation to Application, University of Toronto, Toronto, ONM5G 2A2, Canada
- Max Planck-University of Toronto Center for Neural Science and Technology, University of Toronto, Toronto, ONM5S 3G8, Canada
| | - Jérémie Lefebvre
- Krembil Brain Institute, Division of Clinical and Computational Neuroscience, University Health Network, Toronto, ONM5T 0S8, Canada
- Department of Biology, University of Ottawa, Ottawa, ONK1N 6N5, Canada
- Department of Mathematics, University of Toronto, Toronto, ONM5S 2E4, Canada
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Phillips ET. The synchronizing role of multiplexing noise: Exploring Kuramoto oscillators and breathing chimeras. CHAOS (WOODBURY, N.Y.) 2023; 33:073140. [PMID: 37463090 DOI: 10.1063/5.0135528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2022] [Accepted: 06/02/2023] [Indexed: 07/20/2023]
Abstract
The synchronization of spatiotemporal patterns in a two-layer multiplex network of identical Kuramoto phase oscillators is studied, where each layer is a non-locally coupled ring. Particular focus is on the role played by a noisy inter-layer communication. It is shown that modulating the inter-layer coupling strength by uncommon noise has a significant impact on the dynamics of the network, in particular, that modulating the interlayer coupling by noise can counter-intuitively induce synchronization in networks. It is further shown that increasing the noise intensity has many other analogous effects to that of increasing the interlayer coupling strength. For example, the noise intensity can also induce state transitions in a similar way, in some cases causing the layers to completely synchronize within themselves. It is discussed how such disturbances may in many cases be beneficial to multilayer systems. These effects are demonstrated both for white noise and for other kinds of colored noise. A "floating" breathing chimera state is also discovered in this system.
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De S, Gupta S, Janaki MS, Sekar Iyengar AN. Frequency and wavelet based analyses of partial and complete measure synchronization in a system of three nonlinearly coupled oscillators. CHAOS (WOODBURY, N.Y.) 2018; 28:113108. [PMID: 30501204 DOI: 10.1063/1.5049800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2018] [Accepted: 10/17/2018] [Indexed: 06/09/2023]
Abstract
Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regime is sought from the power spectral analysis. The existence of PMS is confirmed using the order parameter M (here M α β for different combination pairs of oscillators), best suited to identify MS in coupled two-oscillator systems, and this definition is extended to obtain a new order parameter, M 3 , aiding to distinguish complete MS of three oscillators from other forms of motion. The study of wavelet coefficient spectra sheds new light on the relative phase information of the oscillators in the QP PMS regions, also highlighting the intertwined role played by the various frequency components and their amplitudes as they vary temporally. Furthermore, this technique helps to draw a sharp distinction between CMS and chaotic unsynchronized states. Based on the Continuous Wavelet Transform coefficients of the three oscillators, an order parameter M w a v is defined to indicate the extent of synchronization of the various scales (frequencies) for different coupling strengths in the chaotic regime.
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Affiliation(s)
- Sadhitro De
- Department of Physical Sciences, Indian Institute of Science, Bengaluru 560012, India
| | - Shraddha Gupta
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - M S Janaki
- Plasma Physics Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata 700064, India
| | - A N Sekar Iyengar
- Plasma Physics Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata 700064, India
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Lameu EL, Yanchuk S, Macau EEN, Borges FS, Iarosz KC, Caldas IL, Protachevicz PR, Borges RR, Viana RL, Szezech JD, Batista AM, Kurths J. Recurrence quantification analysis for the identification of burst phase synchronisation. CHAOS (WOODBURY, N.Y.) 2018; 28:085701. [PMID: 30180612 DOI: 10.1063/1.5024324] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Accepted: 03/22/2018] [Indexed: 06/08/2023]
Abstract
In this work, we apply the spatial recurrence quantification analysis (RQA) to identify chaotic burst phase synchronisation in networks. We consider one neural network with small-world topology and another one composed of small-world subnetworks. The neuron dynamics is described by the Rulkov map, which is a two-dimensional map that has been used to model chaotic bursting neurons. We show that with the use of spatial RQA, it is possible to identify groups of synchronised neurons and determine their size. For the single network, we obtain an analytical expression for the spatial recurrence rate using a Gaussian approximation. In clustered networks, the spatial RQA allows the identification of phase synchronisation among neurons within and between the subnetworks. Our results imply that RQA can serve as a useful tool for studying phase synchronisation even in networks of networks.
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Affiliation(s)
- E L Lameu
- National Institute for Space Research, São José dos Campos, São Paulo 12227-010, Brazil
| | - S Yanchuk
- Institute of Mathematics, Technical University of Berlin, Berlin 10623, Germany
| | - E E N Macau
- National Institute for Space Research, São José dos Campos, São Paulo 12227-010, Brazil
| | - F S Borges
- Center for Mathematics, Computation, and Cognition, Federal University of ABC, São Bernardo do Campo, São Paulo 09606-045, Brazil
| | - K C Iarosz
- Department of Physics, Humboldt University, Berlin 12489, Germany
| | - I L Caldas
- Institute of Physics, University of São Paulo, São Paulo 05508-900, Brazil
| | - P R Protachevicz
- Program of Post-graduation in Science, State University of Ponta Grossa, Ponta Grossa, Paraná 84030-900, Brazil
| | - R R Borges
- Department of Mathematics, Federal University of Technology-Paraná, Ponta Grossa, Paraná 84016-210, Brazil
| | - R L Viana
- Department of Physics, Federal University of Paraná, Curitiba, Paraná 80060-000, Brazil
| | - J D Szezech
- Program of Post-graduation in Science, State University of Ponta Grossa, Ponta Grossa, Paraná 84030-900, Brazil
| | - A M Batista
- Institute of Physics, University of São Paulo, São Paulo 05508-900, Brazil
| | - J Kurths
- Department of Physics, Humboldt University, Berlin 12489, Germany
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Wang C, Grebogi C, Baptista MS. One node driving synchronisation. Sci Rep 2015; 5:18091. [PMID: 26656718 PMCID: PMC4676025 DOI: 10.1038/srep18091] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2015] [Accepted: 11/11/2015] [Indexed: 11/28/2022] Open
Abstract
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with heterogeneous coupling strengths. The synchronisation of phase-oscillators is independent of the distribution of the natural frequencies, weakly depends on the network size, but highly depends on only one key oscillator whose ratio between its natural frequency in a rotating frame and its coupling strength is maximum. This result is based on a novel method to calculate the critical coupling strength with which the phase-oscillators emerge into frequency synchronisation. In addition, we put forward an analytical method to approximately calculate the phase-angles for the synchronous oscillators.
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Affiliation(s)
- Chengwei Wang
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, AB24 3UE, UK
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, AB24 3UE, UK
| | - Murilo S Baptista
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, AB24 3UE, UK
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