Reduction Methodology for Fluctuation Driven Population Dynamics

Denis S. Goldobin, Matteo di Volo, and Alessandro Torcini
Phys. Rev. Lett. 127, 038301 – Published 13 July 2021
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Abstract

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions due to the divergence of all the moments (cumulants). We have solved this problem by introducing a “pseudocumulants” expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsic and endogenous fluctuations, thus obtaining a unified mean-field formulation encompassing quenched and dynamical sources of disorder.

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  • Received 21 December 2020
  • Revised 24 March 2021
  • Accepted 14 June 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.038301

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & ThermodynamicsInterdisciplinary PhysicsNetworksPhysics of Living Systems

Authors & Affiliations

Denis S. Goldobin1,2, Matteo di Volo3, and Alessandro Torcini3,4,5,*

  • 1Institute of Continuous Media Mechanics, Ural Branch of RAS, Acad. Korolev Street 1, 614013 Perm, Russia
  • 2Department of Theoretical Physics, Perm State University, Bukirev Street 15, 614990 Perm, Russia
  • 3Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089, 95302 Cergy-Pontoise cedex, France
  • 4CNR—Consiglio Nazionale delle Ricerche—Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
  • 5INFN Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, Florence, Italy

  • *Corresponding author. alessandro.torcini@cyu.fr

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Issue

Vol. 127, Iss. 3 — 16 July 2021

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