Discrete-Time Chaotic Maps Featuring Hidden Chaotic Attractors

This work introduces autonomous chaotic discrete-time maps corresponding to systems with no fixed point, with a stable fixed point, with a curve of fixed points and with a surface of fixed points. All four chaotic maps exhibit hidden chaotic attractors. Identifying hidden attractors is challenging since information about fixed points does not assist in attractor localization, and the attractor is hidden for computational purposes. The existence of chaotic attractors is demonstrated with phase portraits, basin of attraction diagrams, bifurcation diagrams, approximate entropy and Lyapunov exponent spectrums. The presented maps featuring hidden chaotic attractors can play significant roles in practical engineering problems.