English

On a hypercycle equation with infinitely many members

Populations and Evolution 2022-07-12 v1

Abstract

A hypercycle equation with infinitely many types of macromolecules is formulated and studied both analytically and numerically. The resulting model is given by an integro-differential equation of the mixed type. Sufficient conditions for the existence, uniqueness, and non-negativity of solutions are formulated and proved. Analytical evidence is provided for the existence of non-uniform (with respect to the second variable) steady states. Finally, numerical simulations strongly indicate the existence of a stable nonlinear wave in the form of the wave train.

Keywords

Cite

@article{arxiv.2207.05033,
  title  = {On a hypercycle equation with infinitely many members},
  author = {Alexander S. Bratus and Olga S. Chmereva and Ivan Yegorov and Artem S. Novozhilov},
  journal= {arXiv preprint arXiv:2207.05033},
  year   = {2022}
}

Comments

21 pages, 5 figures

R2 v1 2026-06-25T00:49:17.434Z