What question did this study set out to answer?

The aim is to develop a mathematical framework that combines linear and oscillatory principles to better model complex environmental systems.

March 26, 2026Open Access

A Hybrid Linear-Oscillatory Framework for System Dynamics.

Key Points

The aim is to develop a mathematical framework that combines linear and oscillatory principles to better model complex environmental systems.
Introduced the Universal Oscillating Path as a recursive mathematical framework.
Integrated a Logarithmic Translator to manage exponential complexity.
Used dynamic feedback loops to address stochastic shocks (White Events).
Facilitated multi-stage modelling with iterative feedback mechanisms.
Established a new approach linking linear stability with chaotic behaviors.
Demonstrated how the model effectively manages complex environmental fluctuations.
Found that the recursive framework improves prediction accuracy in dynamic systems.

Abstract

This paper presents the Universal Oscillating Path, a recursive mathematical framework based on the premise that the linear equation (𝒚 = 𝒎𝒙 + 𝒃) constitutes the fundamental structural unit of all physical laws. While classical systems maintain linear stability, complex environmental systems exhibit chaotic fluctuations. This model bridges the gap by integrating a Logarithmic Translator to linearize exponential complexity and a dynamic feedback loop to account for White Events (stochastic shocks). The framework is designed for multi-stage modelling where the output of one linear iteration serves as the input for the next, representing continuous environmental feedback loops.

A Hybrid Linear-Oscillatory Framework for System Dynamics.

Key Points

Abstract

Cite This Study

Also Consider

Also Consider