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Martineau S, Saffold T, Chang TT, Ronellenfitsch H. Enhancing Synchronization by Optimal Correlated Noise. PHYSICAL REVIEW LETTERS 2022; 128:098301. [PMID: 35302804 DOI: 10.1103/physrevlett.128.098301] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Revised: 01/11/2022] [Accepted: 02/09/2022] [Indexed: 06/14/2023]
Abstract
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world networks are under the influence of noisy, random inputs, potentially inhibiting synchronization. While noise is unavoidable, here we show that there exist optimal noise patterns which minimize desynchronizing effects and even enhance order. Specifically, using analytical arguments we show that in the case of a two-oscillator model, there exists a sharp transition from a regime where the optimal synchrony-enhancing noise is perfectly anticorrelated, to one where the optimal noise is correlated. More generally, we then use numerical optimization methods to demonstrate that there exist anticorrelated noise patterns that optimally enhance synchronization in large complex oscillator networks. Our results may have implications in networks such as power grids and neuronal networks, which are subject to significant amounts of correlated input noise.
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Affiliation(s)
- Sherwood Martineau
- Physics Department, Williams College, 33 Lab Campus Drive, Williamstown, Massachusetts 01267, USA
| | - Tim Saffold
- Physics Department, Williams College, 33 Lab Campus Drive, Williamstown, Massachusetts 01267, USA
| | - Timothy T Chang
- Physics Department, Williams College, 33 Lab Campus Drive, Williamstown, Massachusetts 01267, USA
| | - Henrik Ronellenfitsch
- Physics Department, Williams College, 33 Lab Campus Drive, Williamstown, Massachusetts 01267, USA
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Nakao H, Yamaguchi K, Katayama S, Yanagita T. Sparse optimization of mutual synchronization in collectively oscillating networks. CHAOS (WOODBURY, N.Y.) 2021; 31:063113. [PMID: 34241311 DOI: 10.1063/5.0049091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Accepted: 05/14/2021] [Indexed: 06/13/2023]
Abstract
We consider a pair of collectively oscillating networks of dynamical elements and optimize their internetwork coupling for efficient mutual synchronization based on the phase reduction theory developed by Nakao et al. [Chaos 28, 045103 (2018)]. The dynamical equations describing a pair of weakly coupled networks are reduced to a pair of coupled phase equations, and the linear stability of the synchronized state between the networks is represented as a function of the internetwork coupling matrix. We seek the optimal coupling by minimizing the Frobenius and L1 norms of the internetwork coupling matrix for the prescribed linear stability of the synchronized state. Depending on the norm, either a dense or sparse internetwork coupling yielding efficient mutual synchronization of the networks is obtained. In particular, a sparse yet resilient internetwork coupling is obtained by L1-norm optimization with additional constraints on the individual connection weights.
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Affiliation(s)
- Hiroya Nakao
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
| | - Katsunori Yamaguchi
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
| | - Shingo Katayama
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
| | - Tatsuo Yanagita
- Department of Engineering Science, Osaka Electro-Communication University, Neyagawa, Osaka 572-8530, Japan
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Shirasaka S, Watanabe N, Kawamura Y, Nakao H. Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling. Phys Rev E 2017; 96:012223. [PMID: 29347076 DOI: 10.1103/physreve.96.012223] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2017] [Indexed: 12/22/2022]
Abstract
We consider optimization of the linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On the basis of the phase reduction theory, we derive the coupling matrix between different components of the oscillator states that maximizes the linear stability of the synchronized state under given constraints on the overall coupling intensity and the stationary phase difference. The improvement in the linear stability is illustrated by using several types of limit-cycle oscillators as examples.
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Affiliation(s)
- Sho Shirasaka
- Research Center for Advanced Science and Technology, University of Tokyo, Tokyo 153-8904, Japan
| | - Nobuhiro Watanabe
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
| | - Yoji Kawamura
- Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan
| | - Hiroya Nakao
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.,Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, USA
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Yanagita T, Ichinomiya T. Thermodynamic characterization of synchronization-optimized oscillator networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062914. [PMID: 25615171 DOI: 10.1103/physreve.90.062914] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2014] [Indexed: 06/04/2023]
Abstract
We consider a canonical ensemble of synchronization-optimized networks of identical oscillators under external noise. By performing a Markov chain Monte Carlo simulation using the Kirchhoff index, i.e., the sum of the inverse eigenvalues of the Laplacian matrix (as a graph Hamiltonian of the network), we construct more than 1,000 different synchronization-optimized networks. We then show that the transition from star to core-periphery structure depends on the connectivity of the network, and is characterized by the node degree variance of the synchronization-optimized ensemble. We find that thermodynamic properties such as heat capacity show anomalies for sparse networks.
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Affiliation(s)
- Tatsuo Yanagita
- Department of Engineering Science, Osaka Electro-Communication University, Neyagawa 572-8530, Japan
| | - Takashi Ichinomiya
- Department of Biomedical Informatics, Gifu University School of Medicine, 1-1 Yanagido, Gifu, Gifu 501-1194, Japan
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Kaluza P, Mikhailov AS. Autonomous learning by simple dynamical systems with delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:030901. [PMID: 25314384 DOI: 10.1103/physreve.90.030901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2014] [Indexed: 06/04/2023]
Abstract
A general scheme for the construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the dynamics towards the target performance. As an example, a system of coupled phase oscillators, which can, by changing the weights of connections between its elements, evolve to a dynamical state with the prescribed (low or high) synchronization level, is considered and investigated.
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Affiliation(s)
- Pablo Kaluza
- National Scientific and Technical Research Council and Faculty of Exact and Natural Sciences, National University of Cuyo, Padre Contreras 1300, 5500 Mendoza, Argentina and Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
| | - Alexander S Mikhailov
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
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Bhat HS, Vaz GJ. Frequency response and gap tuning for nonlinear electrical oscillator networks. PLoS One 2013; 8:e78009. [PMID: 24223751 PMCID: PMC3817173 DOI: 10.1371/journal.pone.0078009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2013] [Accepted: 09/10/2013] [Indexed: 11/30/2022] Open
Abstract
We study nonlinear electrical oscillator networks, the smallest example of which consists of a voltage-dependent capacitor, an inductor, and a resistor driven by a pure tone source. By allowing the network topology to be that of any connected graph, such circuits generalize spatially discrete nonlinear transmission lines/lattices that have proven useful in high-frequency analog devices. For such networks, we develop two algorithms to compute the steady-state response when a subset of nodes are driven at the same fixed frequency. The algorithms we devise are orders of magnitude more accurate and efficient than stepping towards the steady-state using a standard numerical integrator. We seek to enhance a given network's nonlinear behavior by altering the eigenvalues of the graph Laplacian, i.e., the resonances of the linearized system. We develop a Newton-type method that solves for the network inductances such that the graph Laplacian achieves a desired set of eigenvalues; this method enables one to move the eigenvalues while keeping the network topology fixed. Running numerical experiments using three different random graph models, we show that shrinking the gap between the graph Laplacian's first two eigenvalues dramatically improves a network's ability to (i) transfer energy to higher harmonics, and (ii) generate large-amplitude signals. Our results shed light on the relationship between a network's structure, encoded by the graph Laplacian, and its function, defined in this case by the presence of strongly nonlinear effects in the frequency response.
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Affiliation(s)
- Harish S. Bhat
- Applied Mathematics Unit, University of California Merced, Merced, California, United States of America
- * E-mail:
| | - Garnet J. Vaz
- Applied Mathematics Unit, University of California Merced, Merced, California, United States of America
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Popovych OV, Yanchuk S, Tass PA. Self-organized noise resistance of oscillatory neural networks with spike timing-dependent plasticity. Sci Rep 2013; 3:2926. [PMID: 24113385 PMCID: PMC4070574 DOI: 10.1038/srep02926] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2013] [Accepted: 09/25/2013] [Indexed: 01/01/2023] Open
Abstract
Intuitively one might expect independent noise to be a powerful tool for desynchronizing a population of synchronized neurons. We here show that, intriguingly, for oscillatory neural populations with adaptive synaptic weights governed by spike timing-dependent plasticity (STDP) the opposite is true. We found that the mean synaptic coupling in such systems increases dynamically in response to the increase of the noise intensity, and there is an optimal noise level, where the amount of synaptic coupling gets maximal in a resonance-like manner as found for the stochastic or coherence resonances, although the mechanism in our case is different. This constitutes a noise-induced self-organization of the synaptic connectivity, which effectively counteracts the desynchronizing impact of independent noise over a wide range of the noise intensity. Given the attempts to counteract neural synchrony underlying tinnitus with noisers and maskers, our results may be of clinical relevance.
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Affiliation(s)
- Oleksandr V. Popovych
- Institute of Neuroscience and Medicine – Neuromodulation (INM-7), Research Center Jülich, 52425 Jülich, Germany
| | - Serhiy Yanchuk
- Institute of Mathematics, Humboldt University of Berlin, 10099 Berlin, Germany
| | - Peter A. Tass
- Institute of Neuroscience and Medicine – Neuromodulation (INM-7), Research Center Jülich, 52425 Jülich, Germany
- Department of Neuromodulation, University of Cologne, 50924 Cologne, Germany
- Clinic for Stereotactic and Functional Neurosurgery, University of Cologne, 50924 Cologne, Germany
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