Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 33 tok/s
Gemini 2.5 Pro 51 tok/s Pro
GPT-5 Medium 24 tok/s Pro
GPT-5 High 26 tok/s Pro
GPT-4o 74 tok/s Pro
Kimi K2 188 tok/s Pro
GPT OSS 120B 362 tok/s Pro
Claude Sonnet 4.5 34 tok/s Pro
2000 character limit reached

Synchronization dynamics of phase oscillators on power grid models (2403.18867v1)

Published 25 Mar 2024 in physics.soc-ph and nlin.CD

Abstract: We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous natural frequencies. We employ the complex-valued order parameter --~a widely-used indicator for phase ordering~-- to assess the synchronization dynamics and observe the order parameter to exhibit either constant or periodic or non-periodic, possibly chaotic temporal evolutions for a given coupling strength but depending on initial conditions and the systems' disorder. Interestingly, both topological and spectral characteristics of the power grids point to a diminished capability of these networks to support a temporarily stable synchronization dynamics. We find non-trivial commonalities between the synchronization dynamics of oscillators on seemingly opposing topologies.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (80)
  1. L. Glass, “Synchronization and rhythmic processes in physiology,” Nature 410, 277–284 (2001).
  2. M. Rosenblum and A. Pikovsky, “Synchronization: from pendulum clocks to chaotic lasers and chemical oscillators,” Contemp. Phys. 44, 401–416 (2003).
  3. M. V. Bennett and R. S. Zukin, “Electrical coupling and neuronal synchronization in the mammalian brain,” Neuron 41, 495–511 (2004).
  4. J. Fell and N. Axmacher, “The role of phase synchronization in memory processes,” Nat. Rev. Neurosci. 12, 105–118 (2011).
  5. A. Pikovsky and M. Rosenblum, “Dynamics of globally coupled oscillators: Progress and perspectives,” Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 097616 (2015).
  6. I. I. Blekhman, Synchronization in science and technology (ASME Press, 1988).
  7. H. Nijmeijer and A. Rodriguez-Angeles, Synchronization of mechanical systems (World Scientific, Singapore, 2003).
  8. M. Kapitaniak, K. Czolczynski, P. Perlikowski, A. Stefanski,  and T. Kapitaniak, “Synchronization of clocks,” Phys. Rep. 517, 1–69 (2012).
  9. A. E. Motter, S. A. Myers, M. Anghel,  and T. Nishikawa, “Spontaneous synchrony in power-grid networks,” Nat. Phys. 9, 191–197 (2013).
  10. F. Dörfler and F. Bullo, “Synchronization in complex networks of phase oscillators: A survey,” Automatica 50, 1539–1564 (2014).
  11. G. Csaba and W. Porod, “Coupled oscillators for computing: A review and perspective,” Appl. Phys. Rev. 7, 011302 (2020).
  12. D. Witthaut, F. Hellmann, J. Kurths, S. Kettemann, H. Meyer-Ortmanns,  and M. Timme, “Collective nonlinear dynamics and self-organization in decentralized power grids,” Rev. Mod. Phys. 94, 015005 (2022).
  13. J. Gómez-Gardeñes, Y. Moreno,  and A. Arenas, “Paths to synchronization on complex networks,” Phys. Rev. Lett. 98, 034101 (2007).
  14. J. Gomez-Gardenes, Y. Moreno,  and A. Arenas, “Synchronizability determined by coupling strengths and topology on complex networks,” Phys. Rev. E 75, 066106 (2007).
  15. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno,  and C. Zhou, “Synchronization in complex networks,” Phys. Rep. 469, 93–153 (2008).
  16. M. Rohden, A. Sorge, D. Witthaut,  and M. Timme, “Impact of network topology on synchrony of oscillatory power grids,” Chaos 24, 013123 (2014).
  17. S. H. Strogatz, “From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators,” Physica D 143, 1–20 (2000).
  18. J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort,  and R. Spigler, “The Kuramoto model: A simple paradigm for synchronization phenomena,” Rev. Mod. Phys. 77, 137–185 (2005).
  19. M. Breakspear, S. Heitmann,  and A. Daffertshofer, “Generative models of cortical oscillations: neurobiological implications of the Kuramoto model,” Front. Human Neurosci. 4, 190 (2010).
  20. F. A. Rodrigues, T. K. D. Peron, P. Ji,  and J. Kurths, “The Kuramoto model in complex networks,” Phys. Rep. 610, 1–98 (2016).
  21. C. Bick, M. Goodfellow, C. R. Laing,  and E. A. Martens, “Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review,” J. Math. Neurosci. 10, 9 (2020).
  22. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer Verlag, Berlin, 1984).
  23. M. Schröder, M. Timme,  and D. Witthaut, “A universal order parameter for synchrony in networks of limit cycle oscillators,” Chaos: An Interdisciplinary Journal of Nonlinear Science 27 (2017).
  24. E. Ott and T. M. Antonsen, “Long time evolution of phase oscillator systems,” Chaos: An interdisciplinary journal of nonlinear science 19, 023117 (2009).
  25. R. E. Mirollo, “The asymptotic behavior of the order parameter for the infinite-N Kuramoto model,” Chaos: An Interdisciplinary Journal of Nonlinear Science 22, 033133 (2012).
  26. C. Bick, M. J. Panaggio,  and E. A. Martens, “Chaos in Kuramoto oscillator networks,” Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 071102 (2018).
  27. L. D. Smith and G. A. Gottwald, ‘‘Chaos in networks of coupled oscillators with multimodal natural frequency distributions,” Chaos: An Interdisciplinary Journal of Nonlinear Science 29, 093127 (2019).
  28. P. Clusella and A. Politi, “Irregular collective dynamics in a Kuramoto–Daido system,” J. Phys. Complex. 2, 014002 (2020).
  29. M. S. Yeung and S. H. Strogatz, “Time delay in the Kuramoto model of coupled oscillators,” Phys. Rev. lett. 82, 648 (1999).
  30. D. Senthilkumar, R. Suresh, J. H. Sheeba, M. Lakshmanan,  and J. Kurths, “Delay-enhanced coherent chaotic oscillations in networks with large disorders,” Phys. Rev. E 84, 066206 (2011).
  31. A. Gjurchinovski, E. Schöll,  and A. Zakharova, “Control of amplitude chimeras by time delay in oscillator networks,” Phys. Rev. E 95, 042218 (2017).
  32. C. Bick, M. Timme, D. Paulikat, D. Rathlev,  and P. Ashwin, “Chaos in symmetric phase oscillator networks,” Phys. Rev. Lett. 107, 244101 (2011).
  33. D. Labavić and H. Meyer-Ortmanns, “Long-period clocks from short-period oscillators,” Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 083103 (2017).
  34. T. Chouzouris, I. Omelchenko, A. Zakharova, J. Hlinka, P. Jiruska,  and E. Schöll, “Chimera states in brain networks: Empirical neural vs. modular fractal connectivity,” Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 045112 (2018).
  35. G. Paolini, M. Ciszak, F. Marino, S. Olmi,  and A. Torcini, “Collective excitability in highly diluted random networks of oscillators,” Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 103108 (2022).
  36. B. Tadić, M. Chutani,  and N. Gupte, “Multiscale fractality in partial phase synchronisation on simplicial complexes around brain hubs,” Chaos, Solitons & Fractals 160, 112201 (2022).
  37. A. Buscarino, M. Frasca, L. V. Gambuzza,  and P. Hövel, “Chimera states in time-varying complex networks,” Phys. Rev. E 91, 022817 (2015).
  38. S. Assenza, R. Gutiérrez, J. Gómez-Gardenes, V. Latora,  and S. Boccaletti, “Emergence of structural patterns out of synchronization in networks with competitive interactions,” Sci. Rep. 1, 99 (2011).
  39. D. Ghosh, M. Frasca, A. Rizzo, S. Majhi, S. Rakshit, K. Alfaro-Bittner,  and S. Boccaletti, “The synchronized dynamics of time-varying networks,” Phys. Rep. 949, 1–63 (2022).
  40. A. Rothkegel and K. Lehnertz, “Recurrent events of synchrony in complex networks of pulse-coupled oscillators,” Europhys. Lett. 95, 38001 (2011).
  41. A. Rothkegel and K. Lehnertz, “Irregular macroscopic dynamics due to chimera states in small-world networks of pulse-coupled oscillators,” New J. Phys. 16, 055006 (2014).
  42. M. Gerster, R. Berner, J. Sawicki, A. Zakharova, A. Škoch, J. Hlinka, K. Lehnertz,  and E. Schöll, “FitzHugh–Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena,” Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 123130 (2020).
  43. B. Boaretto, R. Budzinski, K. Rossi, C. Manchein, T. Prado, U. Feudel,  and S. Lopes, “Bistability in the synchronization of identical neurons,” Phys. Rev. E 104, 024204 (2021).
  44. S. Lee and K. Krischer, “Attracting Poisson chimeras in two-population networks,” Chaos: An Interdisciplinary Journal of Nonlinear Science 31, 113101 (2021).
  45. P. Clusella, B. Pietras,  and E. Montbrió, “Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling,” Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 013105 (2022).
  46. J. Sawicki, L. Hartmann, R. Bader,  and E. Schöll, “Modelling the perception of music in brain network dynamics,” Front. Netw. Physiol. 2, 910920 (2022).
  47. M. Thiele, R. Berner, P. A. Tass, E. Schöll,  and S. Yanchuk, “Asymmetric adaptivity induces recurrent synchronization in complex networks,” Chaos: An Interdisciplinary Journal of Nonlinear Science 33, 023123 (2023).
  48. J. Hörsch, F. Hofmann, D. Schlachtberger,  and T. Brown, “PyPSA-Eur: An open optimisation model of the European transmission system,” Energy Strategy Rev. 22, 207–215 (2018).
  49. J. Hörsch, F. Neumann, F. Hofmann, D. Schlachtberger, M. Frysztacki, J. Hampp, P. Glaum,  and T. Brown, “PyPSA-Eur: An Open Optimisation Model of the European Transmission System (Dataset),”  (2022).
  50. R. D. Christie, “www.ee.washington.edu/research/pstca/,”  (1999).
  51. Y. Kuramoto, “Self-entrainment of a population of coupled nonlinear oscillators,” in International Symposium on Mathematical Problems in Theoretical Physics, Springer Lecture Notes in Physics, Vol. 39, edited by H. Araki (Springer, New York, 1975) pp. 420–422.
  52. Y. Guo, D. Zhang, Z. Li, Q. Wang,  and D. Yu, “Overviews on the applications of the Kuramoto model in modern power system analysis,” Int. J. Electr. Power Energy Syst. 129, 106804 (2021).
  53. M. Anvari, L. R. Gorjão, M. Timme, D. Witthaut, B. Schäfer,  and H. Kantz, “Stochastic properties of the frequency dynamics in real and synthetic power grids,” Phys. Rev. Res. 2, 013339 (2020).
  54. L. Rydin Gorjão, R. Jumar, H. Maass, V. Hagenmeyer, G. C. Yalcin, J. Kruse, M. Timme, C. Beck, D. Witthaut,  and B. Schäfer, “Open database analysis of scaling and spatio-temporal properties of power grid frequencies,” Nature Commun. 11, 6362 (2020).
  55. B. Schäfer, L. R. Gorjão, G. C. Yalcin, E. Förstner, R. Jumar, H. Maass, U. Kühnapfel,  and V. Hagenmeyer, “Microscopic fluctuations in power-grid frequency recordings at the sub-second scale,” Complexity 2023, 2657039 (2023).
  56. R. Kutil, “Biased and unbiased estimation of the circular mean resultant length and its variance,” Statistics 46, 549–561 (2012).
  57. G. A. Pagani and M. Aiello, “The power grid as a complex network: a survey,” Physica A: Statistical Mechanics and its Applications 392, 2688–2700 (2013).
  58. A. M. Amani and M. Jalili, “Power grids as complex networks: Resilience and reliability analysis,” IEEE Access 9, 119010–119031 (2021).
  59. G. Ódor, S. Deng, B. Hartmann,  and J. Kelling, “Synchronization dynamics on power grids in Europe and the United States,” Phys. Rev. E 106, 034311 (2022).
  60. D. J. Watts and S. H. Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature 393, 440–442 (1998).
  61. R. Albert and A.-L. Barabási, “Statistical mechanics of complex networks,” Rev. Mod. Phys. 74, 47–97 (2002).
  62. P. Erdős and A. Rényi, “On random graphs I,” Publ. Math. Debrecen 6, 290–297 (1959).
  63. R. Johnsonbaugh and M. Kalin, “A graph generation software package,” in Proceedings of the twenty-second SIGCSE technical symposium on Computer Science Education (1991) pp. 151–154.
  64. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez,  and D.-U. Hwang, “Complex networks: Structure and dynamics,” Phys. Rep. 424, 175–308 (2006).
  65. M. E. J. Newman, “The structure and function of complex networks,” SIAM Rev. 45, 167–256 (2003).
  66. A. E. Motter, C. Zhou,  and J. Kurths, “Network synchronization, diffusion, and the paradox of heterogeneity,” Phys. Rev. E 71, 016116 (2005).
  67. M. di Bernardo, F. Garofalo,  and F. Sorrentino, “Effects of degree correlation on the synchronization of networks of oscillators,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 3499–3506 (2007).
  68. L. M. Pecora and T. L. Carroll, “Master stability functions for synchronized coupled systems,” Phys. Rev. Lett. 80, 2109–2112 (1998).
  69. M. Barahona and L. M. Pecora, “Synchronization in small-world systems,” Phys. Rev. Lett. 89, 054101 (2002).
  70. L. Donetti, P. I. Hurtado,  and M. A. Munoz, “Entangled networks, synchronization, and optimal network topology,” Phys. Rev. Lett. 95, 188701 (2005).
  71. F. M. Atay, T. Bıyıkoğlu,  and J. Jost, “Network synchronization: Spectral versus statistical properties,” Physica D 224, 35–41 (2006).
  72. E. Cotilla-Sanchez, P. D. Hines, C. Barrows,  and S. Blumsack, “Comparing the topological and electrical structure of the North American electric power infrastructure,” IEEE Syst. J. 6, 616–626 (2012).
  73. M. A. S. Monfared, M. Jalili,  and Z. Alipour, “Topology and vulnerability of the Iranian power grid,” Physica A: Statistical Mechanics and its Applications 406, 24–33 (2014).
  74. R. Espejo, S. Lumbreras,  and A. Ramos, “Analysis of transmission-power-grid topology and scalability, the European case study,” Physica A: Statistical Mechanics and its Applications 509, 383–395 (2018).
  75. B. Hartmann and V. Sugár, “Searching for small-world and scale-free behaviour in long-term historical data of a real-world power grid,” Sci. Rep. 11, 6575 (2021).
  76. G. Ansmann, “A highly specific test for periodicity,” Chaos 25, 113106 (2015).
  77. B. Wang, H. Suzuki,  and K. Aihara, “Enhancing synchronization stability in a multi-area power grid,” Sci. Rep. 6, 26596 (2016).
  78. E. B. T. Tchuisseu, D. Gomila, P. Colet, D. Witthaut, M. Timme,  and B. Schäfer, “Curing Braess’ paradox by secondary control in power grids,” New J. Phys. 20, 083005 (2018).
  79. K. V. Mardia and P. E. Jupp, Directional Statistics (Wiley, New York, 2000).
  80. C. C. Gong, C. Zheng, R. Toenjes,  and A. Pikovsky, “Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise,” Chaos: An Interdisciplinary Journal of Nonlinear Science 29, 033127 (2019).

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

This paper has been mentioned in 1 post and received 0 likes.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up to View

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

Explore Trending Papers

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube