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Information propagation in predator-prey dynamics of turbulent plasma

Tomohiro Tanogami1, Makoto Sasaki2, and Tatsuya Kobayashi3,4

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Phys. Rev. E 113, 035201 – Published 3 March, 2026

DOI: https://doi.org/10.1103/p31r-2y55

Abstract

Magnetically confined fusion plasmas exhibit predator-prey-like cyclic oscillations through the self-regulating interaction between drift-wave turbulence and zonal flow. To elucidate the detailed mechanism and causality underlying this phenomenon, we construct a simple stochastic predator-prey model that incorporates intrinsic fluctuations and analyze its statistical properties from an information-theoretic perspective. We first show that the model exhibits persistent fluctuating cyclic oscillations called quasicycles due to amplification of intrinsic noise. This result suggests the possibility that the previously observed periodic oscillations in a toroidal plasma are not limit cycles, but quasicycles, and that such quasicycles may be widely observed under various conditions. For this model, we further prove that information of the zonal flow is propagated to turbulence. This result suggests that turbulence behavior may be predictable to a certain extent based on zonal flow characteristics.

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References (61)

  1. R. M. May, Stability and Complexity in Model Ecosystems (Princeton University, Princeton, NJ, 1973).
  2. J. Maynard-Smith, Models in Ecology (Cambridge University, Cambridge, England, 1974).
  3. J. D. Murray, Mathematical Biology: I. An Introduction, Interdisciplinary Applied Mathematics, Vol. 17 (Springer, Berlin, 2007).
  4. C. Xue and N. Goldenfeld, Stochastic predator-prey dynamics of transposons in the human genome, Phys. Rev. Lett. 117, 208101 (2016).
  5. H.-Y. Shih, T.-L. Hsieh, and N. Goldenfeld, Ecological collapse and the emergence of traveling waves at the onset of shear turbulence, Nat. Phys. 12, 245 (2016).
  6. H.-Y. Shih, Spatial-temporal patterns in evolutionary ecology and fluid turbulence, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2017.
  7. N. Goldenfeld and H.-Y. Shih, Turbulence as a problem in non-equilibrium statistical mechanics, J. Stat. Phys. 167, 575 (2017).
  8. X. Wang, H.-Y. Shih, and N. Goldenfeld, Stochastic model for quasi-one-dimensional transitional turbulence with streamwise shear interactions, Phys. Rev. Lett. 129, 034501 (2022).
  9. T. Nadolny, C. Bruder, and M. Brunelli, Nonreciprocal synchronization of active quantum spins, Phys. Rev. X 15, 011010 (2025).
  10. P. H. Diamond, S. Itoh, K. Itoh, and T. Hahm, Zonal flows in plasma―a review, Plasma Phys. Control. Fusion 47, R35 (2005).
  11. K. Itoh, S.-I. Itoh, P. Diamond, T. Hahm, A. Fujisawa, G. Tynan, M. Yagi, and Y. Nagashima, Physics of zonal flows, Phys. Plasmas 13, 055502 (2006).
  12. K. Itoh, S.-I. Itoh, and A. Fujisawa, An assessment of limit cycle oscillation dynamics prior to L-H transition, Plasma Fusion Res. 8, 1102168 (2013).
  13. Ö. D. Gürcan and P. Diamond, Zonal flows and pattern formation, J. Phys. A 48, 293001 (2015).
  14. T. Estrada, T. Happel, C. Hidalgo, E. Ascasibar, and E. Blanco, Experimental observation of coupling between turbulence and sheared flows during L-H transitions in a toroidal plasma, Europhys. Lett. 92, 35001 (2010).
  15. G. D. Conway, C. Angioni, F. Ryter, P. Sauter, J. Vicente, (ASDEX Upgrade Team), Mean and oscillating plasma flows and turbulence interactions across the L-H confinement transition, Phys. Rev. Lett. 106, 065001 (2011).
  16. L. Schmitz, L. Zeng, T. L. Rhodes, J. C. Hillesheim, E. J. Doyle, R. J. Groebner, W. A. Peebles, K. H. Burrell, and G. Wang, Role of zonal flow predator-prey oscillations in triggering the transition to H-mode confinement, Phys. Rev. Lett. 108, 155002 (2012).
  17. J. Cheng, J. Q. Dong, K. Itoh, L. W. Yan, M. Xu, K. J. Zhao, W. Y. Hong, Z. H. Huang, X. Q. Ji, W. L. Zhong, D. L. Yu, S. I. Itoh, L. Nie, D. F. Kong, T. Lan, A. D. Liu, X. L. Zou, Q. W. Yang, X. T. Ding, X. R. Duan, and Y. Liu, Dynamics of low-intermediate–high-confinement transitions in toroidal plasmas, Phys. Rev. Lett. 110, 265002 (2013).
  18. T. Kobayashi, K. Itoh, T. Ido, K. Kamiya, S.-I. Itoh, Y. Miura, Y. Nagashima, A. Fujisawa, S. Inagaki, K. Ida, et al., Spatiotemporal structures of edge limit-cycle oscillation before L-to-H transition in the JFT-2M tokamak, Phys. Rev. Lett. 111, 035002 (2013).
  19. J. Bizarro, X. Litaudon, T. Tala, and J. E. Contributors, Controlling the internal transport barrier oscillations in high-performance tokamak plasmas with a dominant fraction of bootstrap current, Nucl. Fusion 47, L41 (2007).
  20. T. Kobayashi, M. Kobayashi, Y. Narushima, Y. Suzuki, K. Y. Watanabe, K. Mukai, and Y. Hayashi, Self-sustained divertor oscillation driven by magnetic island dynamics in torus plasma, Phys. Rev. Lett. 128, 085001 (2022).
  21. P. H. Diamond, Y.-M. Liang, B. A. Carreras, and P. W. Terry, Self-regulating shear flow turbulence: A paradigm for the L to H transition, Phys. Rev. Lett. 72, 2565 (1994).
  22. A. J. McKane and T. J. Newman, Predator-prey cycles from resonant amplification of demographic stochasticity, Phys. Rev. Lett. 94, 218102 (2005).
  23. A. J. Black and A. J. McKane, Stochastic formulation of ecological models and their applications, Trends Ecol. Evol. 27, 337 (2012).
  24. T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85, 461 (2000).
  25. B. P. Van Milligen, G. Birkenmeier, M. Ramisch, T. Estrada, C. Hidalgo, and A. Alonso, Causality detection and turbulence in fusion plasmas, Nucl. Fusion 54, 023011 (2014).
  26. E.-j. Kim and R. Hollerbach, Time-dependent probability density functions and information geometry of the low-to-high confinement transition in fusion plasma, Phys. Rev. Res. 2, 023077 (2020).
  27. R. Hollerbach, E.-j. Kim, and L. Schmitz, Time-dependent probability density functions and information diagnostics in forward and backward processes in a stochastic prey–predator model of fusion plasmas, Phys. Plasmas 27, 102301 (2020).
  28. E.-j. Kim and R. Hollerbach, Non-equilibrium statistical properties, path-dependent information geometry, and entropy relations in edge-localized modes in fusion plasmas, Phys. Plasmas 29, 112302 (2022).
  29. E.-J. Kim and A. A. Thiruthummal, Stochastic dynamics of fusion low-to-high confinement mode (LH) transition: Correlation and causal analyses using information geometry, Entropy 26, 17 (2023).
  30. P. Fuller, E.-j. Kim, R. Hollerbach, and B. Hnat, Time-dependent probability density functions, information geometry and entropy production in a stochastic prey-predator model of fusion plasmas, Phys. Plasmas 30, 102502 (2023).
  31. P. Fuller, E.-j. Kim, R. Hollerbach, and B. Hnat, Time-dependent probability density functions and information geometry in a stochastic prey-predator model of fusion plasmas, Phys. Plasmas 31, 092506 (2024).
  32. E.-J. Kim and A. A. Thiruthummal, Nonperturbative theory of the low-to-high confinement transition through stochastic simulations and information geometry: Correlation and causal analyses, Phys. Rev. E 110, 045209 (2024).
  33. E.-j. Kim and A. A. Thiruthummal, Probabilistic theory of the L-H transition and causality, Plasma Phys. Control. Fusion 67, 025025 (2025).
  34. A. E. Allahverdyan, D. Janzing, and G. Mahler, Thermodynamic efficiency of information and heat flow, J. Stat. Mech. (2009) P09011.
  35. J. M. Horowitz and M. Esposito, Thermodynamics with continuous information flow, Phys. Rev. X 4, 031015 (2014).
  36. J. M. Parrondo, J. M. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  37. R. Chetrite, M. L. Rosinberg, T. Sagawa, and G. Tarjus, Information thermodynamics for interacting stochastic systems without bipartite structure, J. Stat. Mech. (2019) 114002.
  38. L. Peliti and S. Pigolotti, Stochastic Thermodynamics: An Introduction (Princeton University, Princeton, NJ, 2021).
  39. N. Shiraishi, An Introduction to Stochastic Thermodynamics: From Basic to Advanced, Fundamental Theories of Physics, Vol. 212 (Springer Nature, Berlin, 2023).
  40. T. Tanogami and R. Araki, Information-thermodynamic bound on information flow in turbulent cascade, Phys. Rev. Res. 6, 013090 (2024).
  41. T. Tanogami, Scale locality of information flow in shell models of turbulence, J. Stat. Mech. (2025) 093405.
  42. T. Tanogami and R. Araki, Scale-to-scale information flow amplifies turbulent fluctuations, Phys. Rev. Res. 7, 023078 (2025).
  43. M. Pineda-Krch, H. J. Blok, U. Dieckmann, and M. Doebeli, A tale of two cycles—distinguishing quasi-cycles and limit cycles in finite predator–prey populations, Oikos 116, 53 (2007).
  44. T. Butler and N. Goldenfeld, Fluctuation-driven Turing patterns, Phys. Rev. E 84, 011112 (2011).
  45. R. Rao and M. Esposito, Conservation laws and work fluctuation relations in chemical reaction networks, J. Chem. Phys. 149, 245101 (2018).
  46. M. Vellela and H. Qian, A quasistationary analysis of a stochastic chemical reaction: Keizer's paradox, Bull. Math. Biol. 69, 1727 (2007).
  47. G. Falasco and M. Esposito, Macroscopic stochastic thermodynamics, Rev. Mod. Phys. 97, 015002 (2025).
  48. V. Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1992).
  49. C. W. Gardiner, Handbook of Stochastic Methods, 4th ed. (Springer, Berlin, 2009).
  50. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1996).
  51. P. Manz, M. Ramisch, and U. Stroth, Long-range correlations induced by the self-regulation of zonal flows and drift-wave turbulence, Phys. Rev. E 82, 056403 (2010).
  52. P. Manz, G. Xu, B. Wan, H. Wang, H. Guo, I. Cziegler, N. Fedorczak, C. Holland, S. Müller, S. Thakur, et al., Zonal flow triggers the L-H transition in the experimental advanced superconducting tokamak, Phys. Plasmas 19, 072311 (2012).
  53. M. Cavedon, T. Pütterich, E. Viezzer, G. Birkenmeier, T. Happel, F. Laggner, P. Manz, F. Ryter, U. Stroth, A. U. Team, et al., Interplay between turbulence, neoclassical and zonal flows during the transition from low to high confinement mode at ASDEX Upgrade, Nucl. Fusion 57, 014002 (2017).
  54. S. Kobayashi, Ö. D. Gürcan, and P. H. Diamond, Direct identification of predator-prey dynamics in gyrokinetic simulations, Phys. Plasmas 22, 090702 (2015).
  55. D. A. Smirnov, Spurious causalities with transfer entropy, Phys. Rev. E 87, 042917 (2013).
  56. R. G. James, N. Barnett, and J. P. Crutchfield, Information flows? A critique of transfer entropies, Phys. Rev. Lett. 116, 238701 (2016).
  57. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley-Interscience, Hoboken, NJ, 2006).
  58. A. Hasegawa and M. Wakatani, Plasma edge turbulence, Phys. Rev. Lett. 50, 682 (1983).
  59. G. Sugihara, R. May, H. Ye, C.-h. Hsieh, E. Deyle, M. Fogarty, and S. Munch, Detecting causality in complex ecosystems, Science 338, 496 (2012).
  60. N. Dumérat, R. Sarkis, G. E. Tovar, and M. Ramisch, Causal coupling of edge-SOL coherent structures with zonal flows, Plasma Phys. Control. Fusion 67, 115010 (2025).
  61. E. W. J. Wallace, D. T. Gillespie, K. R. Sanft, and L. R. Petzold, Linear noise approximation is valid over limited times for any chemical system that is sufficiently large, IET Syst. Biol. 6, 102 (2012).

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Phys. Rev. E 113, 035201– Published 3 March, 2026
  • Received 7 August 2025
  • Accepted 9 February 2026
Article part of CHORUS
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