English

Time evolution of a mean-field generalized contact process

Probability 2022-02-23 v1 Disordered Systems and Neural Networks Statistical Mechanics Adaptation and Self-Organizing Systems Populations and Evolution

Abstract

We investigate the macroscopic time evolution and stationary states of a mean field generalized contact process in Rd\mathbb{R}^d. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a model of neurons with discrete voltages evolving by a stochastic integrate and fire mechanism. We obtain a complete solution in the spatially uniform case and partial solutions in the general case. The system has one or more fixed points and also traveling wave solutions.

Keywords

Cite

@article{arxiv.2108.00264,
  title  = {Time evolution of a mean-field generalized contact process},
  author = {Logan Chariker and Joel Lebowitz},
  journal= {arXiv preprint arXiv:2108.00264},
  year   = {2022}
}

Comments

20 pages, 2 figures

R2 v1 2026-06-24T04:42:58.931Z