Chaotic system with a singular plane: chaotic dynamics, blow-up behavior, and degeneration assessment

Chaotic systems attract significant attention due to the rich dynamics induced by their nonlinear terms. While most existing systems are constructed using continuous nonlinear functions, chaotic models involving singularities remain largely unexplored. To bridge this gap, this paper introduces a novel chaotic system with a Singular Plane (SP). The dynamics analysis proves the chaotic nature of this system. Owing to the presence of the SP, the system exhibits two distinct types of Lyapunov exponent (LE) behaviors depending on the initial conditions. Furthermore, a modified version of the system is proposed to observe blow-up behavior and investigate how trajectories approach or cross the SP, a phenomenon rarely reported in other chaotic systems. The original system is then implemented on an FPGA platform, and its hardware-level performance is thoroughly evaluated. Finally, the period–precision rate is introduced to quantify the degree of chaos degradation in hardware implementations, providing practical guidance for selecting appropriate data precision in chaos-based applications.