Mechanics Analysis and Hardware Implementation of a New 3D Chaotic System

Abstract

In this study, a new 3D chaotic system was first transformed into a Kolmogorov-type system to describe the vector field from the viewpoint of torque. In this Kolmogorov-type system, only inertial torque and non-Rayleigh dissipation exist. Thus, this is different from previously reported Kolmogorov-type systems that are generally decomposed into inertial torque, internal torque, dissipation, and external torque. Moreover, by analyzing these two torques, the physical background of the system and the key factors of chaos generation were also determined. That is, the inertial torque and non-Rayleigh dissipation are responsible for chaos generation in the new 3D chaotic system. Then, the Casimir function and Hamiltonian energy function were also analyzed to investigate the cycling of energy in the chaotic system. Finally, both an analog circuit and a Field Programmable Gate Array (FPGA) circuit were designed to implement the chaotic system. All of the experimentally obtained results are consistent with the results of numerical analysis, which did not only indicate the chaotic characteristics of the 3D chaotic system physically, but also provided physical models for engineering applications.