A Novel Chaotic Map Based on Decay Functions and Its Applications
Motivated by decay-modulated nonlinear perturbations in discrete dynamical systems, this paper proposes a one-dimensional Sine-Bessel chaotic map by coupling the sine map with the zeroth-order Bessel function of the first kind. Fixed-point analysis establishes a bounded positively invariant interval, guarantees the existence of at least one fixed point, and provides a local stability criterion. Numerical investigations based on attractors, bifurcation diagrams, Lyapunov exponents, spectral entropy, and autocorrelation demonstrate that the map exhibits broad chaotic parameter regions and reduced periodic windows compared with the classical Sine map. Under synchronous translation of the two phase parameters, recurrent yet nonidentical bifurcation and Lyapunov-exponent structures are observed, revealing parameter-translation symmetry breaking caused by the nonperiodic decay term. Further comparisons among different decay functions show that the fixed-translation difference determines the persistence of structural deformation, while oscillation governs its alternating form. Finally, a pseudorandom number generator is constructed, and its output passed the adopted NIST SP 800-22 statistical criteria.