Robust Parameter Interval Identification for a Logistic-Type Fractional Difference System

Classical integer-order chaotic maps usually exhibit chaotic degradation under prolonged iterations or finite-precision computation, which may compromise the reliability of chaos-based algorithms. Fractional difference chaotic systems with memory effects offer a promising alternative; however, existing studies rarely provide a systematic and quantitative understanding of how the nonlinear gain parameter, memory strength, and initial condition collectively influence the emergence and robustness of complex dynamics under finite-time iterations. It should be noted that memory effects do not inherently guarantee robust chaotic behavior under finite-precision computation, and appropriate parameter and initial-condition selection remains essential. In this paper, we conduct a systematic numerical dynamical analysis of a logistic-type fractional difference system with power-law memory by leveraging bifurcation diagrams and Lyapunov exponent mappings. Rather than aiming to select optimal parameter points, we propose a quantitative composite chaos evaluation (CCE) framework to identify admissible parameter intervals within which robust finite-time chaotic dynamics can be consistently sustained. Numerical results demonstrate the effectiveness and reliability of the proposed framework, which may facilitate future applications in chaos-enhanced optimization, nonlinear control, and secure communication.