A non-autonomous conservative system and its reconstitution in integral domain

Non-autonomous conservative system with time-dependent stimulus has rarely been studied in literature. In this paper, we present a two-dimensional non-autonomous conservative system. It belongs to the category of non-Hamiltonian conservative system, and its dynamical properties are uncovered by kinetic and energy-based analyses. Nested chaotic and quasi-periodic motions, which are volume-conservative but not energy-conservative, are observed under different initial conditions. The topological structures of these conservative motions are closely related to the isoenergetic lines of the governing Hamiltonian function. Furthermore, this non-autonomous conservative system is reconstituted in integral domain. Based on the reformed time-varying equilibrium points and isoenergetic lines, the reconstituted conservative motions are further analyzed. Finally, PSIM circuit simulations are performed to verify the reconstituted conservative motions in the integral domain. As can be seen, the characteristics of the volume-conservative motions are thoroughly interpreted in the original and integral state variable domains.