Exponential Change Characteristics of State Variables and Circuit Simulation of Classical Autonomous Systems

Investigating the chaotic characteristics of classical autonomous systems necessitates prioritizing the dynamic behavior of simple system models, which plays a crucial role in advancing research in this field. This study examines the influence of exponential variations in state variables on the dynamic behavior of chaotic systems, using a classical chaotic system as the main research case. Using classical autonomous systems as the examples, three possible scenarios of exponential change in state variables are listed and the chaotic characteristics of the system under these conditions are demonstrated. The system model exhibits a wide range of chaotic characteristics under different conditions. Additionally, the exponential change of state variables is applied to a simplified chaotic system to illustrate the universality of this phenomenon. Finally, circuit simulation experiments confirm the feasibility of circuit simulations for chaotic system models with exponential change characteristics of state variables, providing theoretical support for the application of such chaotic systems.