Original scientific paper

https://doi.org/10.7906/indecs.24.6.6

Mathematical Formalisation of Emergent Behaviour in Digital Twins of Manufacturing Systems

Sergiy V. Kovalevskyy ; Donbas State Engineering Academy, Kramаtorsk-Khust, Ukraine *

* Corresponding author.

Abstract

The rapid development of digital twin technology has created new opportunities for modelling and optimisation of complex manufacturing systems. However, most existing studies treat digital twins primarily as simulation tools and seldom address emergent behaviour arising from subsystem interactions. Emergence is a fundamental property of complex systems in which global behaviour cannot be reduced to the sum of individual component behaviours. This article proposes a mathematical framework for analysing emergent behaviour in digital twins of manufacturing systems. The digital twin is modelled as a dynamic network of interacting subsystems described by a system of differential equations. An entropy-based emergence index is introduced to quantify collective complexity. Two stability theorems and one optimality theorem are formally proved. A variational Principle of Minimum Emergent Complexity is formulated, linking information-theoretic complexity directly to manufacturing efficiency. Numerical simulations with four scientific figures confirm the theoretical predictions. The proposed formalisation provides a foundation for intelligent control in Industry 5.0 environments.

Keywords

digital twin; complex systems; emergence; manufacturing systems; entropy

Hrčak ID:

350259

URI

https://hrcak.srce.hr/350259

Publication date:

30.12.2026.

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