Dynamical behaviors of a chaotic system with no equilibria

Based on Sprott D system, a simple three-dimensional autonomous system with no equilibria is reported. The remarkable particularity of the system is that there exists a constant controller, which can adjust the type of chaotic attractors. It is demonstrated to be chaotic in the sense of having a positive largest Lyapunov exponent and fractional dimension. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcation diagram, Poincaré mapping and period-doubling route to chaos are analyzed with careful numerical simulations.

► A simple 3D autonomous system with no equilibria is reported.
► A constant controller can adjust the type of chaotic attractors.
► The chaotic attractors are distinctly different from those of the existing chaotic attractors.
► Period-doubling route to chaos are analyzed with careful numerical simulations.