@article{3c47ee22-1709-4e1b-a862-c59c969c8099,
  abstract     = {{<p>We present an exact dimensional reduction for ensembles of N identical dynamical units governed by ordinary differential equations of order M with quasi-linear structure. In these systems, each unit follows a linear differential equation whose coefficients depend nonlinearly on the ensemble of variables, such as a mean field, giving rise to a large class of network dynamical systems. We derive M+1 closed-form macroscopic equations of order M with variables that exactly capture the full microscopic dynamics and that allow for the exact reconstruction of individual trajectories from the reduced system. This dimensional reduction facilitates a simplified analysis of collective behavior in a new class of coupled oscillator networks and provides computationally efficient exact representations of large-scale dynamics. We illustrate our approach on two examples, highlighting new families of solvable models relevant to physics, biology, and engineering that are now amenable to simplified analysis.</p>}},
  author       = {{Augustsson, Felix and Martens, Erik A. and Cestnik, Rok}},
  issn         = {{1089-7682}},
  language     = {{eng}},
  month        = {{04}},
  number       = {{4}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{Chaos (Woodbury, N.Y.)}},
  title        = {{Exact dimensional reduction for quasi-linear ODE ensembles}},
  url          = {{http://dx.doi.org/10.1063/5.0291571}},
  doi          = {{10.1063/5.0291571}},
  volume       = {{36}},
  year         = {{2026}},
}