Improved Transistor-Based Fractional Exponentiation Circuit for Chaotic Oscillators

This research focuses on improving the transistor-based fractional exponentiation circuit (also known as 444 circuit). It aims to address the issue of insufficient stability and verifies the adaptability of the chaotic system through hardware experiments. Starting from three feedback capacitors as the improvement point, mathematical modeling analysis and circuit simulation verification effectively improve the system's bandwidth and dynamic response characteristics. The optimized circuit is embedded in the VB5 system, constructing a series of chaotic systems with nonlinear feedback. The chaotic phase trajectories obtained from experimental observations are highly consistent with the theoretical predictions, providing key empirical evidence for the improvement of the stability of the 444 circuit. This research achievement opens up a low-cost technical implementation path for the realization of complex nonlinear feedback, such as fractional exponent operation in chaotic circuits.