A Unique Family of Cyclic Symmetric Chaotic Systems with Energy-Dependent Divergence, Full-Variables Offset-Boosting, and Total Amplitude Control

This paper proposes a new family of third-order circulant chaotic systems characterized by an (Casimir) energy-dependent rate of volume contraction, enabling dynamic control over its dissipative properties. Each of the new systems is obtained using three- or five-segment nonlinearities as well as nonlinear dissipation. The energy-dependent mechanism introduces a tunable dissipation factor that influences the evolution of system trajectories, providing new insights into chaos regulation. Through analytical modeling and numerical simulation, we explore how offset boosting and amplitude control can be effectively employed to modulate the system’s chaotic attractors without destroying their intrinsic nonlinear behavior. An experimental study validates the theoretical predictions, demonstrating that precise adjustment of offset and amplitude parameters allows for real-time manipulation of chaotic states. The results highlight the potential of circulant chaotic systems for applications in secure communication, signal processing, and adaptive control systems.