Quadratic Stochastic Operators: Results and Open Problems

TL;DR

This paper reviews the history, recent developments, and open problems in quadratic stochastic operators, highlighting their significance across various scientific fields and the need for further research.

Contribution

It provides a comprehensive overview of quadratic stochastic operators, summarizes key results, and discusses unresolved questions in the field.

Findings

Historical development of quadratic stochastic operators

Recent applications in mathematics, biology, and physics

Identification of open problems for future research

Abstract

The history of the quadratic stochastic operators can be traced back to work of S.Bernshtein (1924). During more than 80 years this theory developed and many papers were published. In recent years it has again become of interest in connection with numerous applications to many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems.