Research on shape-controllable generalized multi-cluster Hamiltonian conservative chaotic flow systems and their FPGA implementation

This study delves into the utilization of Hamiltonian energy in generalized conservative chaotic systems, innovatively constructing a class of shape-controllable generalized multi-cluster Hamiltonian conservative chaotic flow systems. The uniqueness of these systems lies in their existence on hyper-surfaces dependent on Hamiltonian energy, thus realizing controllability in shape. Through numerical analysis, we investigated the dynamic characteristics of these novel systems and found that as the number of flow clusters increases, the maximum Lyapunov exponent of the system significantly enhances, indicating an intensified level of chaos and an augmented sensitivity to initial conditions. Furthermore, this study successfully implements shape-controllable multi-cluster generalized Hamiltonian conservative chaos using FPGA hardware circuits. This not only verifies the existence of multi-cluster chaotic flow dynamics at the physical level but also provides new tools and resources for fields such as communication systems, cryptography, and others that require highly complex signals, opening up novel possibilities for future technological innovations.