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The paper reports a new generalized Hamiltonian chaotic system with transient quasi-periodic flows and intermittent chaos by investigating the Kolmogorov-type transformation for a 3D chaotic system. The new system meets Hamiltonian energy conservation when [Formula: see text], and it is always conservative in volume because of a zero divergence. In addition, its Hamiltonian energy is found to be only related to the initial points. Subsequently, some dynamics analyses are presented to investigate its conservative characteristics and coexisting flows including periodic flows, quasi-periodic flows, and chaotic flows. Besides, both transient quasi-periodic flows and intermittent chaos are also found to occur, which further shows complex dynamics of the new generalized Hamiltonian chaotic system. Finally, an FPGA circuit is designed to implement the new generalized Hamiltonian chaotic system, and the results from the circuit experiments are consistent with those from numerical analyses. Complex dynamic characteristics existing in the new generalized Hamiltonian chaotic system seem more appropriate to be used in image encryption and secure communication. And the FPGA circuit not only shows the new generalized Hamiltonian chaotic system from a physical viewpoint, but also provides a new pseudo-random signal generator for engineering applications.

In this study, first, the phenomenon of multistability in the Lü system is found, which shows the coexistence of two different point attractors and one chaotic attractor. These coexisting attractors are dependent on initial conditions of the system while the parameters of the system are fixed. Then, the Lü system is transformed to a Kolmogorov-type system, which includes the conservative torque consisting of the inertial torque and the internal torque, the dissipative torque, and the external torque. Moreover, by analyzing the combination of different types of torques and investigating the cycling of energy based on the Casimir function and Hamiltonian function, the interaction between the external torque and other torques is found to be the main reason for the Lü system to generate chaos. Finally, by investigating the Casimir function, it is found that the boundary of the Lü system is only related to system parameters.

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