Abstract
This paper presents a new four-dimension autonomous system which shows extraordinary dynamical
properties . Chaotic attractor and periodic attractor or hyper-chaotic attractor and quasi-periodic attractor,
which are governed by different initial conditions instead of the system parameters, can coexist in the
deterministic system. These interesting phenomena are verified through numerical simulations and analyses
including time series, phase portraits, Poincaré maps, bifurcation diagrams, and Lyapunov exponents.