A Chen-Like Model: High Periodicity Leading to Chaotic Dynamics

The Chen circuit system, a three-dimensional autonomous system with intriguing dynamics, has gained considerable attention due to its potential applications in diverse scientific fields. In this article, a Chen-like system is defined and a comprehensive dynamics studied. The system exhibits chaotic dynamics, limit cycles, and bifurcations, making it a captivating subject of study. By employing numerical simulations and analytical techniques, we explore the system's stability and identify critical parameter values leading to qualitative changes. Notably, we delve into Hopf bifurcations, which give rise to stability changes and the emergence of limit cycles. Furthermore, we analyze the fractal dimension of the system's attractor, providing insights into its complexity and self-similarity. Through a systematic examination of the Chen-like system, we deepen our understanding of its intricate dynamics and offer valuable insights into the underlying mechanisms. The findings contribute to the field of dynamical systems and hold potential implications in areas such as chaos-based secure communications, signal processing, and nonlinear control. This work serves as a valuable reference for researchers and practitioners interested in the dynamics and bifurcation analysis of nonlinear systems.