A Fractional-Order Improved Quantum Logistic Map: Chaos, 0-1 Testing, Complexity, and Control

Based on a quantum logistic map and Caputo-like delta difference operator, fractional-order improved map, which has hidden attractors, was constructed. Its dynamical behaviors are investigated by employing phase portraits, bifurcation diagrams, Lyapunov spectra, mapping, 0-1 testing. It is shown that the proposed influenced both parameters fractional order. Then, complexity of explored through spectral entropy approximate entropy. The results show stronger robustness within chaos higher complexity, so it more suitable for engineering applications. In addition, chaotic can be controlled different periodic orbits nonlinear mapping wavelet function.