Nonlinear Dynamic Behavior of Two Distinct Chaotic Systems

Abstract

The nonlinear dynamics of two chaotic systems, namely the optoelectronic feedback (OEFB) and the Lu-Chen electronic chaotic system, are simulated and implemented in this work using the Berkeley Madonna software. Control parameters and initial conditions have been adjusted to demonstrate transitions from one state to another. Upon modifying certain regulating elements, both systems exhibited excessive sensitivity to initial conditions and displayed dynamic nonlinear behavior. The OEFB system reveals a homoclinic condition with a Shilnikov attractor as the feedback intensity increases. In contrast, the Lu-Chen system exhibits sensitivity to parameters a, b, and c, accompanied by multiscroll behavior, as evidenced by time series, the Fast Fourier Transform (FFT), and attractor analysis. These results offer potential applications, including data encoding, secure communications, and image processing. This research studied the properties of two different chaotic dynamical systems. These two chaotic systems are optoelectronic feedback and Chua systems. The results are analyzed, and it is found that the behavior of the Chua system changes in the time series, which in turn causes the attractor to change. The results showed a significant increase in the Chua system's bandwidth. Studying the different characteristics opens a broad scope for many applications, the most important of which is secure communications.