Conservative chaos and invariant tori in the modified Sprott A system

Generally, there are few volume-conservative but not energy-conservative chaotic systems in the literature. By recomposing the skew-symmetric state matrix of the Sprott A system, a new volume-conservative chaotic system is coined in this paper. We mainly focus on investigating its dynamical behaviors that relay on the external excitation k, which directly determines the number of equilibria of the system. Without k, there exist two lines of equilibria that can be degenerated into two or four equilibria for the given nonzero initial conditions, while with k, the system is a no-equilibrium system that can produce conservative chaos and invariant tori for different initial conditions. Moreover, these rich dynamical behaviors are illustrated by several numerical techniques including time series, phase portraits, Poincaré sections, bifurcation diagrams and Lyapunov exponents.