Published June 6, 2026 | Version v2
Preprint Open

Trixe (T) Dynamics: A Mathematical Framework for Information Transformation from Probabilistic Chaos to Absolute Determinism

Authors/Creators

  • 1. Independent Researcher

Description

This paper introduces the Trixe (T) model, a mathematical framework designed to map the transformation of information from probabilistic chaos (<Xe) to absolute determinism (>Xe). By employing a tripartite architecture consisting of stabilization mechanisms via the Orbital Variable (Ov) and transition pathways (0Xe), the model demonstrates the asymptotic decay of variance through bidirectional coupling and bifurcation analysis. This research bridges the gap between stochastic fluctuations and predictive deterministic outputs.

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Additional details

Related works

Is identical to
Preprint: https://www.academia.edu/165174934/Trixe_T_Dynamics_A_Mathematical_Framework_for_Information_Transformation_from_Probabilistic_Chaos_to_Absolute_Determinism (URL)
Is supplemented by
Software: https://github.com/zerghirsaw/Trixe-Theory/tree/main/test (URL)

Dates

Submitted
2026-06-06

Software

Repository URL
https://github.com/zerghirsaw/Trixe-Theory
Programming language
Python
Development Status
Active

References

  • Guckenheimer, J., & Holmes, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag.
  • Haken, H. (1983). Synergetics: An Introduction and Advanced Topics. Springer-Verlag.
  • Langevin, P. (1908). Sur la théorie du mouvement brownien. Comptes Rendus de l'Académie des Sciences, 146(1), 530-533.
  • Lemons, D. S., & Gythiel, A. (1997). Paul Langevin's 1908 paper on the theory of Brownian motion. American Journal of Physics, 65(11), 1079-1081.
  • Prigogine, I. (1977). Time, Structure and Fluctuations. Nobel Lecture, 261-275.
  • Risken, H. (1989). The Fokker-Planck Equation: Methods of Solution and Applications (2nd ed.). Springer.
  • Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27(3), 379-423.
  • Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Westview Press.
  • Chen, Y., et al. (2021). Active noise suppression in stochastic dynamical System. IEEE Transactions on Automatic Control, 66(12), 5890-5905.
  • Kappen, H. J. (2022). Optimal control theory and the transition l to determinism. Jurnal of Statistical Mechanics, 2022(8), 083201.