Linear model with time-varying interactions

Paper Title:

Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder

Published on:

8 May 2024

Primary Category:

Disordered Systems and Neural Networks

Paper Authors:

Francesco Ferraro,

Christian Grilletta,

Amos Maritan,

Samir Suweis,

Sandro Azaele

Bullets

Key Details

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Proposes model with large set of linear differential equations

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Interactions between components fluctuate randomly in time

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Applies Dynamical Mean Field Theory to find exact solution

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Interaction time-scale impacts system variability non-monotonically

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Phase diagram maps stationary versus divergent regimes

Explore the topics in this paper

dynamical systems

mathematical models

mean field theory

phase transitions

stochastic processes

AI generated summary

Linear model with time-varying interactions

This paper introduces a mathematical model with multiple interacting components, where the interaction strengths vary randomly over time. The authors apply an analytical technique called Dynamical Mean Field Theory to find an exact solution for the model's behavior. Key results describe how the system's variability and stability depend on the time-scale of the fluctuating interactions in non-trivial ways. For some parameters, slower interaction fluctuations counterintuitively destabilize the system. The analytical solution also enables mapping a phase diagram delineating when the system reaches a stationary state versus when component variables diverge.