A new conservative system with isolated invariant tori and six-cluster chaotic flows

Based on the matrix differential equation of the Sprott-A system, this paper presents a class of rare 3D conservative systems by adjusting its skew-symmetric state matrix and Hamiltonian. Then, an example system is reported to show the conservative dynamical behaviors. For given parameters and initial conditions, the example system can generate six isolated invariant tori and six-cluster conservative chaotic flows. Numerical results show that the six isolated invariant tori are located in six isolated isosurfaces, while the six-cluster conservative chaotic flows approximately run on an interconnected isosurface. Moreover, it is found that the shape and number of invariant tori and conservative chaotic flows relay on the Hamiltonian of the example system.