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Razavi S, Wong F, Abubaker-Sharif B, Matsubayashi HT, Nakamura H, Nguyen NTH, Robinson DN, Chen B, Iglesias PA, Inoue T. Synthetic control of actin polymerization and symmetry breaking in active protocells. SCIENCE ADVANCES 2024; 10:eadk9731. [PMID: 38865458 PMCID: PMC11168455 DOI: 10.1126/sciadv.adk9731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Accepted: 05/08/2024] [Indexed: 06/14/2024]
Abstract
Nonlinear biomolecular interactions on membranes drive membrane remodeling crucial for biological processes including chemotaxis, cytokinesis, and endocytosis. The complexity of biomolecular interactions, their redundancy, and the importance of spatiotemporal context in membrane organization impede understanding of the physical principles governing membrane mechanics. Developing a minimal in vitro system that mimics molecular signaling and membrane remodeling while maintaining physiological fidelity poses a major challenge. Inspired by chemotaxis, we reconstructed chemically regulated actin polymerization inside vesicles, guiding membrane self-organization. An external, undirected chemical input induced directed actin polymerization and membrane deformation uncorrelated with upstream biochemical cues, suggesting symmetry breaking. A biophysical model incorporating actin dynamics and membrane mechanics proposes that uneven actin distributions cause nonlinear membrane deformations, consistent with experimental findings. This protocellular system illuminates the interplay between actin dynamics and membrane shape during symmetry breaking, offering insights into chemotaxis and other cell biological processes.
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Affiliation(s)
- Shiva Razavi
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Felix Wong
- Institute for Medical Engineering and Science, Department of Biological Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
- Infectious Disease and Microbiome Program, Broad Institute of MIT and Harvard, Cambridge, MA 02139, USA
| | - Bedri Abubaker-Sharif
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Hideaki T. Matsubayashi
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Hideki Nakamura
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Nhung Thi Hong Nguyen
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Douglas N. Robinson
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Baoyu Chen
- Roy J. Carver Department of Biochemistry, Biophysics and Molecular Biology, Iowa State University, Ames, IA 50011, USA
| | - Pablo A. Iglesias
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Takanari Inoue
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
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2
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Razavi S, Wong F, Abubaker-Sharif B, Matsubayashi HT, Nakamura H, Sandoval E, Robinson DN, Chen B, Liu J, Iglesias PA, Inoue T. Synthetic control of actin polymerization and symmetry breaking in active protocells. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.09.22.559060. [PMID: 37790449 PMCID: PMC10542490 DOI: 10.1101/2023.09.22.559060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/05/2023]
Abstract
Non-linear biomolecular interactions on the membranes drive membrane remodeling that underlies fundamental biological processes including chemotaxis, cytokinesis, and endocytosis. The multitude of biomolecules, the redundancy in their interactions, and the importance of spatiotemporal context in membrane organization hampers understanding the physical principles governing membrane mechanics. A minimal, in vitro system that models the functional interactions between molecular signaling and membrane remodeling, while remaining faithful to cellular physiology and geometry is powerful yet remains unachieved. Here, inspired by the biophysical processes underpinning chemotaxis, we reconstituted externally-controlled actin polymerization inside giant unilamellar vesicles, guiding self-organization on the membrane. We show that applying undirected external chemical inputs to this system results in directed actin polymerization and membrane deformation that are uncorrelated with upstream biochemical cues, indicating symmetry breaking. A biophysical model of the dynamics and mechanics of both actin polymerization and membrane shape suggests that inhomogeneous distributions of actin generate membrane shape deformations in a non-linear fashion, a prediction consistent with experimental measurements and subsequent local perturbations. The active protocellular system demonstrates the interplay between actin dynamics and membrane shape in a symmetry breaking context that is relevant to chemotaxis and a suite of other biological processes.
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Affiliation(s)
- Shiva Razavi
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Felix Wong
- Institute for Medical Engineering & Science, Department of Biological Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
- Infectious Disease and Microbiome Program, Broad Institute of MIT and Harvard, Cambridge, MA 02139, USA
| | - Bedri Abubaker-Sharif
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Hideaki T. Matsubayashi
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Hideki Nakamura
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Eduardo Sandoval
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Douglas N. Robinson
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Baoyu Chen
- Roy J. Carver Department of Biochemistry, Biophysics and Molecular Biology, Iowa State University, Ames, IA 50011, USA
| | - Jian Liu
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Pablo A. Iglesias
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Electrical and Computer Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Takanari Inoue
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
- Department of Cell Biology, Center for Cell Dynamics, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
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3
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Goldmann M, Fischer I, Mirasso CR, C Soriano M. Exploiting oscillatory dynamics of delay systems for reservoir computing. CHAOS (WOODBURY, N.Y.) 2023; 33:093139. [PMID: 37748487 DOI: 10.1063/5.0156494] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Accepted: 09/05/2023] [Indexed: 09/27/2023]
Abstract
Nonlinear dynamical systems exhibiting inherent memory can process temporal information by exploiting their responses to input drives. Reservoir computing is a prominent approach to leverage this ability for time-series forecasting. The computational capabilities of analog computing systems often depend on both the dynamical regime of the system and the input drive. Most studies have focused on systems exhibiting a stable fixed-point solution in the absence of input. Here, we go beyond that limitation, investigating the computational capabilities of a paradigmatic delay system in three different dynamical regimes. The system we chose has an Ikeda-type nonlinearity and exhibits fixed point, bistable, and limit-cycle dynamics in the absence of input. When driving the system, new input-driven dynamics emerge from the autonomous ones featuring characteristic properties. Here, we show that it is feasible to attain consistent responses across all three regimes, which is an essential prerequisite for the successful execution of the tasks. Furthermore, we demonstrate that we can exploit all three regimes in two time-series forecasting tasks, showcasing the versatility of this paradigmatic delay system in an analog computing context. In all tasks, the lowest prediction errors were obtained in the regime that exhibits limit-cycle dynamics in the undriven reservoir. To gain further insights, we analyzed the diverse time-distributed node responses generated in the three regimes of the undriven system. An increase in the effective dimensionality of the reservoir response is shown to affect the prediction error, as also fine-tuning of the distribution of nonlinear responses. Finally, we demonstrate that a trade-off between prediction accuracy and computational speed is possible in our continuous delay systems. Our results not only provide valuable insights into the computational capabilities of complex dynamical systems but also open a new perspective on enhancing the potential of analog computing systems implemented on various hardware platforms.
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Affiliation(s)
- Mirko Goldmann
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Ingo Fischer
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Claudio R Mirasso
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Miguel C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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4
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Buccellato A, Çatal Y, Bisiacchi P, Zang D, Zilio F, Wang Z, Qi Z, Zheng R, Xu Z, Wu X, Del Felice A, Mao Y, Northoff G. Probing Intrinsic Neural Timescales in EEG with an Information-Theory Inspired Approach: Permutation Entropy Time Delay Estimation (PE-TD). ENTROPY (BASEL, SWITZERLAND) 2023; 25:1086. [PMID: 37510033 PMCID: PMC10378026 DOI: 10.3390/e25071086] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Revised: 07/10/2023] [Accepted: 07/14/2023] [Indexed: 07/30/2023]
Abstract
Time delays are a signature of many physical systems, including the brain, and considerably shape their dynamics; moreover, they play a key role in consciousness, as postulated by the temporo-spatial theory of consciousness (TTC). However, they are often not known a priori and need to be estimated from time series. In this study, we propose the use of permutation entropy (PE) to estimate time delays from neural time series as a more robust alternative to the widely used autocorrelation window (ACW). In the first part, we demonstrate the validity of this approach on synthetic neural data, and we show its resistance to regimes of nonstationarity in time series. Mirroring yet another example of comparable behavior between different nonlinear systems, permutation entropy-time delay estimation (PE-TD) is also able to measure intrinsic neural timescales (INTs) (temporal windows of neural activity at rest) from hd-EEG human data; additionally, this replication extends to the abnormal prolongation of INT values in disorders of consciousness (DoCs). Surprisingly, the correlation between ACW-0 and PE-TD decreases in a state-dependent manner when consciousness is lost, hinting at potential different regimes of nonstationarity and nonlinearity in conscious/unconscious states, consistent with many current theoretical frameworks on consciousness. In summary, we demonstrate the validity of PE-TD as a tool to extract relevant time scales from neural data; furthermore, given the divergence between ACW and PE-TD specific to DoC subjects, we hint at its potential use for the characterization of conscious states.
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Affiliation(s)
- Andrea Buccellato
- Padova Neuroscience Center, University of Padova, Via Orus 2/B, 35129 Padova, Italy
- Department of General Psychology, University of Padova, Via Venezia, 8, 35131 Padova, Italy
| | - Yasir Çatal
- The Royal's Institute of Mental Health Research & University of Ottawa, Brain and Mind Research Institute, Centre for Neural Dynamics, Faculty of Medicine, University of Ottawa, 145 Carling Avenue, Rm. 6435, Ottawa, ON K1Z 7K4, Canada
| | - Patrizia Bisiacchi
- Padova Neuroscience Center, University of Padova, Via Orus 2/B, 35129 Padova, Italy
- Department of General Psychology, University of Padova, Via Venezia, 8, 35131 Padova, Italy
| | - Di Zang
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai 200040, China
- Shanghai Key Laboratory of Brain Function and Restoration and Neural Regeneration, Shanghai 200040, China
- State Key Laboratory of Medical Neurobiology, MOE Frontiers Center for Brain Science, School of Basic Medical Sciences and Institutes of Brain Science, Fudan University, Shanghai 200032, China
- National Center for Neurological Disorders, Shanghai 200040, China
- Neurosurgical Institute, Fudan University, Shanghai 200040, China
- Shanghai Clinical Medical Center of Neurosurgery, Shanghai 200040, China
| | - Federico Zilio
- Department of Philosophy, Sociology, Education and Applied Psychology, University of Padova, Piazza Capitaniato, 3, 35139 Padova, Italy
| | - Zhe Wang
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai 200040, China
- Shanghai Key Laboratory of Brain Function and Restoration and Neural Regeneration, Shanghai 200040, China
- State Key Laboratory of Medical Neurobiology, MOE Frontiers Center for Brain Science, School of Basic Medical Sciences and Institutes of Brain Science, Fudan University, Shanghai 200032, China
- National Center for Neurological Disorders, Shanghai 200040, China
- Neurosurgical Institute, Fudan University, Shanghai 200040, China
- Shanghai Clinical Medical Center of Neurosurgery, Shanghai 200040, China
| | - Zengxin Qi
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai 200040, China
- Shanghai Key Laboratory of Brain Function and Restoration and Neural Regeneration, Shanghai 200040, China
- State Key Laboratory of Medical Neurobiology, MOE Frontiers Center for Brain Science, School of Basic Medical Sciences and Institutes of Brain Science, Fudan University, Shanghai 200032, China
- National Center for Neurological Disorders, Shanghai 200040, China
- Neurosurgical Institute, Fudan University, Shanghai 200040, China
- Shanghai Clinical Medical Center of Neurosurgery, Shanghai 200040, China
| | - Ruizhe Zheng
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai 200040, China
- Shanghai Key Laboratory of Brain Function and Restoration and Neural Regeneration, Shanghai 200040, China
- State Key Laboratory of Medical Neurobiology, MOE Frontiers Center for Brain Science, School of Basic Medical Sciences and Institutes of Brain Science, Fudan University, Shanghai 200032, China
- National Center for Neurological Disorders, Shanghai 200040, China
- Neurosurgical Institute, Fudan University, Shanghai 200040, China
- Shanghai Clinical Medical Center of Neurosurgery, Shanghai 200040, China
| | - Zeyu Xu
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai 200040, China
- Shanghai Key Laboratory of Brain Function and Restoration and Neural Regeneration, Shanghai 200040, China
- State Key Laboratory of Medical Neurobiology, MOE Frontiers Center for Brain Science, School of Basic Medical Sciences and Institutes of Brain Science, Fudan University, Shanghai 200032, China
- National Center for Neurological Disorders, Shanghai 200040, China
- Neurosurgical Institute, Fudan University, Shanghai 200040, China
- Shanghai Clinical Medical Center of Neurosurgery, Shanghai 200040, China
| | - Xuehai Wu
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai 200040, China
- Shanghai Key Laboratory of Brain Function and Restoration and Neural Regeneration, Shanghai 200040, China
- State Key Laboratory of Medical Neurobiology, MOE Frontiers Center for Brain Science, School of Basic Medical Sciences and Institutes of Brain Science, Fudan University, Shanghai 200032, China
- National Center for Neurological Disorders, Shanghai 200040, China
- Neurosurgical Institute, Fudan University, Shanghai 200040, China
- Shanghai Clinical Medical Center of Neurosurgery, Shanghai 200040, China
| | - Alessandra Del Felice
- Padova Neuroscience Center, University of Padova, Via Orus 2/B, 35129 Padova, Italy
- Department of Neuroscience, Section of Neurology, University of Padova, Via Belzoni, 160, 35121 Padova, Italy
| | - Ying Mao
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai 200040, China
- Shanghai Key Laboratory of Brain Function and Restoration and Neural Regeneration, Shanghai 200040, China
- State Key Laboratory of Medical Neurobiology, MOE Frontiers Center for Brain Science, School of Basic Medical Sciences and Institutes of Brain Science, Fudan University, Shanghai 200032, China
- National Center for Neurological Disorders, Shanghai 200040, China
- Neurosurgical Institute, Fudan University, Shanghai 200040, China
- Shanghai Clinical Medical Center of Neurosurgery, Shanghai 200040, China
| | - Georg Northoff
- The Royal's Institute of Mental Health Research & University of Ottawa, Brain and Mind Research Institute, Centre for Neural Dynamics, Faculty of Medicine, University of Ottawa, 145 Carling Avenue, Rm. 6435, Ottawa, ON K1Z 7K4, Canada
- Mental Health Center, Zhejiang University School of Medicine, Hangzhou 310013, China
- Centre for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou 310013, China
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5
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Keane A, Neff A, Blaha K, Amann A, Hövel P. Transitional cluster dynamics in a model for delay-coupled chemical oscillators. CHAOS (WOODBURY, N.Y.) 2023; 33:2895974. [PMID: 37307156 DOI: 10.1063/5.0147645] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 05/15/2023] [Indexed: 06/14/2023]
Abstract
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in the experimental setup controls the onset of oscillations via a Hopf bifurcation. For a smaller voltage, the oscillators exhibit simple, so-called primary, clustering patterns, where all phase differences between each set of coupled oscillators are identical. However, upon increasing the voltage, secondary states, where phase differences differ, are detected, in addition to the primary states. Previous work on this system saw the development of a mathematical model that explained how the existence, stability, and common frequency of the experimentally observed cluster states could be accurately controlled by the delay time of the coupling. In this study, we revisit the mathematical model of the electrochemical oscillators in order to address open questions by means of bifurcation analysis. Our analysis reveals how the stable cluster states, corresponding to experimental observations, lose their stability via an assortment of bifurcation types. The analysis further reveals complex interconnectedness between branches of different cluster types. We find that each secondary state provides a continuous transition between certain primary states. These connections are explained by studying the phase space and parameter symmetries of the respective states. Furthermore, we show that it is only for a larger value of the voltage parameter that the branches of secondary states develop intervals of stability. For a smaller voltage, all the branches of secondary states are completely unstable and are, therefore, hidden to experimentalists.
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Affiliation(s)
- Andrew Keane
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
- Environmental Research Institute, University College Cork, Cork T23 XE10, Ireland
| | - Alannah Neff
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
| | - Karen Blaha
- Sandia National Labs, 1515 Eubank Blvd SE1515 Eubank Blvd SE, Albuquerque, New Mexico 87123, USA
| | - Andreas Amann
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
| | - Philipp Hövel
- Department of Electrical and Information Engineering, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, 24143 Kiel, Germany
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6
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Müller-Bender D, Radons G. Laminar chaos in systems with quasiperiodic delay. Phys Rev E 2023; 107:014205. [PMID: 36797923 DOI: 10.1103/physreve.107.014205] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 12/15/2022] [Indexed: 06/18/2023]
Abstract
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)]0031-900710.1103/PhysRevLett.120.084102. It is characterized by nearly constant laminar phases, which are periodically interrupted by irregular bursts, where the intensity levels of the laminar phases vary chaotically from phase to phase. In this paper, we demonstrate that laminar chaos can also be observed in systems with quasiperiodic delay, where we generalize the concept of conservative and dissipative delays to such systems. It turns out that the durations of the laminar phases vary quasiperiodically and follow the dynamics of a torus map in contrast to the periodic variation observed for periodic delay. Theoretical and numerical results indicate that introducing a quasiperiodic delay modulation into a time-delay system can lead to a giant reduction of the dimension of the chaotic attractors. By varying the mean delay and keeping other parameters fixed, we found that the Kaplan-Yorke dimension is modulated quasiperiodically over several orders of magnitudes, where the dynamics switches quasiperiodically between different types of high- and low-dimensional types of chaos.
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Affiliation(s)
- David Müller-Bender
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
- ICM - Institute for Mechanical and Industrial Engineering, 09117 Chemnitz, Germany
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7
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Sugitani Y, Konishi K. Amplitude death in delay-coupled oscillators on directed graphs. Phys Rev E 2022; 105:064202. [PMID: 35854497 DOI: 10.1103/physreve.105.064202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Accepted: 05/06/2022] [Indexed: 06/15/2023]
Abstract
The present paper investigates amplitude death (AD) in delay-coupled oscillators on directed graphs, in which the connection delays among oscillators are heterogeneous. We reveal that a linear stability analysis of AD can be significantly simplified by focusing on directed cycles in the graph. First, it is proven that the characteristic function of a steady state can be factorized into several functions that can be analyzed independently. Second, we show that the number of connection parameters to be considered for the stability analysis can be reduced, because the stability depends on the sums of connection delays for directed cycles and is independent of the connection delays on edges that do not form directed cycles. The theoretical results are verified through numerical simulations.
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Affiliation(s)
- Yoshiki Sugitani
- Department of Electrical and Electronic Engineering, Ibaraki University 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan
| | - Keiji Konishi
- Department of Electrical and Information Systems, Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
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8
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Abstract
Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened or aggregated. As the neglected and unresolved terms become important, the utility of model predictions diminishes. We develop a novel, versatile and rigorous methodology to learn non-Markovian closure parametrizations for known-physics/low-fidelity models using data from high-fidelity simulations. The new
neural closure models
augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori–Zwanzig formulation and the inherent delays in complex dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgrid-scale processes in coarse models and augment the simplification of complex biological and physical–biogeochemical models. We find that using non-Markovian over Markovian closures improves long-term prediction accuracy and requires smaller networks. We derive adjoint equations and network architectures needed to efficiently implement the new discrete and distributed nDDEs, for any time-integration schemes and allowing non-uniformly spaced temporal training data. The performance of discrete over distributed delays in closure models is explained using information theory, and we find an optimal amount of past information for a specified architecture. Finally, we analyse computational complexity and explain the limited additional cost due to neural closure models.
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Affiliation(s)
- Abhinav Gupta
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Pierre F. J. Lermusiaux
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
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9
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Cheng G, Zheng S, Dong J, Xu Z, Gui R. Effect of time delay in a bistable synthetic gene network. CHAOS (WOODBURY, N.Y.) 2021; 31:053105. [PMID: 34240922 DOI: 10.1063/5.0046373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 04/12/2021] [Indexed: 06/13/2023]
Abstract
The essence of logical stochastic resonance is the dynamic manipulation of potential wells. The effect of time delay on the depth of potential wells and the width of a bistable region can be inferred by logic operations in the bistable system with time delay. In a time-delayed synthetic gene network, time delay in the synthesis process can increase the depth of the potential wells, while that in the degradation process, it can reduce the depth of the potential wells, which will result in a decrease in the width of the bistable region (the reason for time delay to induce logic operations without external driving force) and the instability of the system (oscillation). These two opposite effects imply stretching and folding, leading to complex dynamical behaviors of the system, including period, chaos, bubble, chaotic bubble, forward and reverse period doubling bifurcation, intermittency, and coexisting attractors.
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Affiliation(s)
- Guanghui Cheng
- Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430048, China
| | - Shutao Zheng
- Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430048, China
| | - Jiahao Dong
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Zhenqin Xu
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Rong Gui
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
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10
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Talla Mbé JH, Woafo P. Study of the effect of the offset phase in time-delay electro-optical systems. CHAOS (WOODBURY, N.Y.) 2020; 30:093130. [PMID: 33003947 DOI: 10.1063/5.0004638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Accepted: 09/02/2020] [Indexed: 06/11/2023]
Abstract
We show that the effect of the offset phase on the dynamics of the time-delay optoelectronic oscillators that is observed experimentally can be explained in terms of switching between the subcritical and supercritical Hopf bifurcations. The domains of the offset phase for which the system functions are determined analytically. We also show that the width of these domains exceptionally depends on the interplay between the three time scales of the system. Our theoretical results fit with the experimental measurements.
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Affiliation(s)
- Jimmi H Talla Mbé
- Laboratory of Condensed Matter, Electronics and Signal Processing, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - Paul Woafo
- Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, Faculty of Science, P. O. Box 812, Yaoundé, Cameroon
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11
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Müller-Bender D, Otto A, Radons G, Hart JD, Roy R. Laminar chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of laminar chaos. Phys Rev E 2020; 101:032213. [PMID: 32289959 DOI: 10.1103/physreve.101.032213] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 02/25/2020] [Indexed: 11/07/2022]
Abstract
Recently, it was shown that certain systems with large time-varying delay exhibit different types of chaos, which are related to two types of time-varying delay: conservative and dissipative delays. The known high-dimensional turbulent chaos is characterized by strong fluctuations. In contrast, the recently discovered low-dimensional laminar chaos is characterized by nearly constant laminar phases with periodic durations and a chaotic variation of the intensity from phase to phase. In this paper we extend our results from our preceding publication [Hart, Roy, Müller-Bender, Otto, and Radons, Phys. Rev. Lett. 123, 154101 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.154101], where it is demonstrated that laminar chaos is a robust phenomenon, which can be observed in experimental systems. We provide a time series analysis toolbox for the detection of robust features of laminar chaos. We benchmark our toolbox by experimental time series and time series of a model system which is described by a nonlinear Langevin equation with time-varying delay. The benchmark is done for different noise strengths for both the experimental system and the model system, where laminar chaos can be detected, even if it is hard to distinguish from turbulent chaos by a visual analysis of the trajectory.
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Affiliation(s)
- David Müller-Bender
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Andreas Otto
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Joseph D Hart
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.,Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Rajarshi Roy
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.,Department of Physics, University of Maryland, College Park, Maryland 20742, USA.,Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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Böttcher PC, Otto A, Kettemann S, Agert C. Time delay effects in the control of synchronous electricity grids. CHAOS (WOODBURY, N.Y.) 2020; 30:013122. [PMID: 32013511 DOI: 10.1063/1.5122738] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2019] [Accepted: 12/23/2019] [Indexed: 06/10/2023]
Abstract
The expansion of inverter-connected generation facilities (i.e., wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change, whereas conventional generation with large rotating generator masses provides stabilizing inertia, inverter-connected generation does not. Since the underlying power system and the control mechanisms that keep it close to a desired reference state were not designed for such a low inertia system, this might make the system vulnerable to disturbances. In this paper, we will investigate whether the currently used control mechanisms are able to keep a low inertia system stable and how this is affected by the time delay between a frequency deviation and the onset of the control action. We integrate the control mechanisms used in Continental Europe into a model of coupled oscillators which resembles the second order Kuramoto model. This model is then used to investigate how the interplay of changing inertia, network topology, and delayed control affects the stability of the interconnected power system. To identify regions in the parameter space that make stable grid operation possible, the linearized system is analyzed to create the system's stability chart. We show that lower and distributed inertia could have a beneficial effect on the stability of the desired synchronous state.
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Affiliation(s)
- Philipp C Böttcher
- DLR-Institute of Networked Energy Systems, Carl-von-Ossietsky Straße 15, 26129 Oldenburg, Germany
| | - Andreas Otto
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Stefan Kettemann
- Department of Physics and Earth Sciences, Jacobs University, Campus Ring 1, 28759 Bremen, Germany
| | - Carsten Agert
- DLR-Institute of Networked Energy Systems, Carl-von-Ossietsky Straße 15, 26129 Oldenburg, Germany
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Hart JD, Roy R, Müller-Bender D, Otto A, Radons G. Laminar Chaos in Experiments: Nonlinear Systems with Time-Varying Delays and Noise. PHYSICAL REVIEW LETTERS 2019; 123:154101. [PMID: 31702295 DOI: 10.1103/physrevlett.123.154101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2019] [Indexed: 06/10/2023]
Abstract
A new type of dynamics called laminar chaos was recently discovered through a theoretical analysis of a scalar delay differential equation with time-varying delay. Laminar chaos is a low-dimensional dynamics characterized by laminar phases of nearly constant intensity with periodic durations and a chaotic variation of the intensity from one laminar phase to the next laminar phase. This is in stark contrast to the typically observed higher-dimensional turbulent chaos, which is characterized by strong fluctuations. In this Letter we provide the first experimental observation of laminar chaos by studying an optoelectronic feedback loop with time-varying delay. The noise inherent in the experiment requires the development of a nonlinear Langevin equation with variable delay. The results show that laminar chaos can be observed in higher-order systems, and that the phenomenon is robust to noise and a digital implementation of the variable time delay.
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Affiliation(s)
- Joseph D Hart
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Rajarshi Roy
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - David Müller-Bender
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Andreas Otto
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
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