Theoretical study on instability of the base solutions of Lorenz system via Ordinary Differential Equations

Abstract

The Lorenz system is well-known for producing chaotic solutions for a particular range of technical systems and process characteristics. To examine the instability, fluctuation parameters in the form of exponential functions are introduced to the base solutions of the ODEs, and numerical and computational methodologies are used to determine the range of values that cause instability under different conditions. This paper will focus on the Lorenz system's instability of Ordinary Differential Equations (ODE) that regulates the thermal-hydrodynamic behavior of a two-dimensional fluid layer which is equally warmed (distributed) from bottom to top. The boundary layer of instability is also examined and compared with numerical and computational methods, and the accuracy of the solutions is thoroughly investigated. The study will give considerable insight into the requirements for stability of numerous technical systems such as DNA analysis, chemical reactors, thermosyphons, Malkus waterwheel, electric circuits, DC motors, pipelines, and power generation using micro as well as nanoscale techniques.