(untitled) (Jagannath University Journal of Science, 2025)
This study investigates approaches for the analytical understanding of chaotic attractors in dynamical systems, with a focus on their dynamic behaviors. Chaotic attractor features non-linear dynamics, complex design, and beginning condition sensitivity. The study examines famous chaotic systems such the Lorenz, Rössler, Duffing, and Chen attractors, as well as modifications to these systems, in an effort to enhance complexity and randomness for secure communications and pseudorandom number generation. The method integrates parameter optimization, simulation, and permutation entropy to measure the intrinsic uncertainty of complex systems. This research studies the actual settings of each attractor and changes their surrounding conditions in great detail to show how little changes can significantly affect failure and recovery. Using chaos inside attractor systems to increase system performance is presented in this work for applications that demand high levels of security and unpredictability, such as encryption, authentication, and secure data transfer. Jagannath University Journal of Science, Volume 11, Number 2, Dec. 2024, pp. 108−125