Ultrametric dynamics for the closed fractal-cluster resource models

TL;DR

This paper introduces an ultrametric-based model for resource distribution dynamics in fractal-cluster systems, describing how resources transfer and reach equilibrium within a structured, organism-like system.

Contribution

It proposes a novel ultrametric model for resource redistribution in fractal-cluster systems, including a general dynamic equation and numerical solutions.

Findings

Numerical solutions for resource transfer dynamics were obtained.

The model captures cluster-specific transfer times based on ultrametric sizes.

Discussion on parameter identification for real systems was included.

Abstract

The evolutional scenario of the resource distribution in the fractal-cluster systems which is identified as an "organism" has been suggested. We propose a model in which the resource redistribution dynamics in the closed system is determined by the ultrametric structure of the system's space. Moreover, each cluster has its own character time of a transfer to the equilibrium state which is determined by the ultrametric size of the cluster. The general equation which determines this dynamics has been written. For the determined type of the resource transitions among clusters, the solution to this equation has been numerically received. The problem of the parameter's identification modeling for the real systems has been discussed.