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Advanced Multivariate Catastrophe Model for Quantitative Analysis of Complex Systems With Case Studies and

Jiamin Niu1, Jiu Hui Wu1

  • 1School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, China.

Annals of the New York Academy of Sciences
|December 23, 2025
PubMed
Summary
This summary is machine-generated.

We developed a multivariate quantitative catastrophe model (MQCM) for predicting state transitions in complex systems. This new framework enables robust quantitative predictions, overcoming limitations of classical catastrophe theory.

Keywords:
blackbody radiationcatastrophe modelingquantitative analysisstructural stability

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Area of Science:

  • Physics
  • Complex Systems Analysis
  • Mathematical Modeling

Background:

  • Quantitative prediction of state transitions in complex systems is a significant scientific challenge.
  • Classical catastrophe theory offers qualitative insights but is limited by dimensionality and its non-quantitative nature.

Purpose of the Study:

  • To introduce the multivariate quantitative catastrophe model (MQCM) for robust, quantitative prediction of state transitions.
  • To extend catastrophe theory's applicability to complex, multivariable systems.

Main Methods:

  • Developed the MQCM by integrating a power-law composite control function into catastrophe theory's topological structure.
  • Ensured dimensional homogeneity as a physical constraint within the model.
  • Utilized singularity analysis for quantitative derivation of physical laws.

Main Results:

  • MQCM successfully predicts state transitions in complex systems, moving beyond qualitative classification.
  • Verified the model's predictive power using blackbody radiation and solid heat capacity.
  • Derived governing physical laws from a single unified formula in asymptotic limits.

Conclusions:

  • MQCM provides a systematic, rigorous, and insightful framework for the quantitative application of catastrophe theory.
  • The model is ideal for systems exhibiting distinct scaling laws around critical points.
  • Opens new avenues for understanding critical phenomena and interdisciplinary applications.