Chaotic Dynamics Derived from the Montgomery Conjecture: Application to Electrical Systems

Abstract

Here, we introduce a novel method for obtaining chaotic dynamics based on the Montgomery conjecture for the pair correlation of zeros of the Riemann zeta function. Motivated by the conjecture, we present a recursive relation that reveals chaotic behavior. Notably, we provide insights into the possible uses of this derived chaotic dynamics in electrical engineering by interpreting it as a unique representation of an electrical system. Furthermore, we investigate the relevance of entropy, bifurcation analysis, and chaos theory in this framework for electrical systems. We look into its applicability to signal processing, stability analysis through bifurcation, and how entropy measures the predictability or unpredictability of electrical signals. Additionally, we discuss the system's strange attractor and its transition to voltage collapse, highlighting the interplay between chaotic dynamics and stability in electrical systems. Furthermore, we analyze the system's energy distribution, taking into account how chaotic dynamics may affect energy allocation or dissipation. Furthermore, we compare the chaotification and Hermiticity of the resulting operators between Yitang dynamics and Montgomery dynamics. To have a better grasp of the spectrum features of each operator, we calculate the eigenvalues for each one obtained from the corresponding dynamics. Our results provide fresh insights into number-theoretic chaotic dynamics and how they might be applied in real-world electrical engineering applications. This work provides encouraging opportunities for further research and technology developments by laying the foundation for creative investigations in system dynamics.