Riemann-Lagrange geometry for starfish-coral dynamical system

TL;DR

This paper develops a Riemann-Lagrange geometric framework to analyze the complex social interaction dynamics in colonial organisms, using advanced geometric tools like nonlinear connections and jet Yang-Mills entities.

Contribution

It introduces a novel geometric approach to model and analyze social interaction systems in colonial organisms, combining Riemann-Lagrange geometry with dynamical systems theory.

Findings

Established a geometric structure for social interaction dynamics

Derived expressions for nonlinear connections, torsions, and curvatures

Connected geometric entities with biological social systems

Abstract

In this paper we develop the Riemann-Lagrange geometry, in the sense of nonlinear connection, d-torsions, d-curvatures and jet Yang-Mills entity, associated with the dynamical system concerning social interaction in colonial organisms.