New classes of quadratic vector fields admitting integral-preserving Kahan-Hirota-Kimura discretizations

TL;DR

This paper introduces new quadratic vector fields for which the Kahan-Hirota-Kimura discretization preserves key features like conserved quantities and invariant measures, even if the systems are not integrable.

Contribution

It identifies novel families of quadratic vector fields with discretizations that maintain important continuous system properties.

Findings

Preservation of conserved quantities in new quadratic vector fields

Invariant measures are maintained under discretization

Discretizations work even for non-integrable systems

Abstract

We present some new families of quadratic vector fields, not necessarily integrable, for which their Kahan-Hirota-Kimura discretization exhibits the preservation of some of the characterizing features of the underlying continuous systems (conserved quantities and invariant measures).