Year: 2025
Type: article
Abstract: This article aims to study parallelizable random dynamical systems by examining them through the terms of dissipation and stochastic Lyapunov functions. It is demonstrated that any random variable that is not a random fixed point admits a tube, and every non-wandering point is within one. The Lyapunov function is employed to characterize the asymptotic stability of compact and closed random sets. The section of a random dynamical system is used to define the parallelizable random dynamical system, and it is proven that a random dynamical system is parallelizable if and only if it admits a section. Furthermore, the principle of Lyapunov used this characterization to study the parallelizability of random dynamical systems. The concept of symmetry is defined, and then its impact on the behavior of stochastic dynamic systems, particularly the Lorenz system, is discussed. In addition, by using an appropriate stochastic Lyapunov function, we have shown that the random Lorenz system is parallelizable.
Source: Symmetry
DOI: 10.3390/sym17030325
Authors: Ihsan Jabbar Kadhim, Asmahan Abed Yasir
Institutions: University of Al-Qadisiyah, Ministry of Education
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4407842616