The main contribution of our work is the further exploration of some novel and counter-intuitive results on nonlinear behaviors of digital filters and provides some analytical analysis for the account of our partial results. The main implications of our results is: (1) one can select initial conditions and design the filter parameters so that chaotic behaviors can be avoided; (2) one can also select the parameters to generate chaos for certain applications, such as chaotic communications, encryption and decryption, fractal coding, etc; (3) we can find out the filter parameters when random-like chaotic patterns exhibited in some local regions on the phase plane by the Shannon entropies
