Dynamical Properties of Two-Dimesional Map with 'Tent' Type Piece Wise Linear Characteristic

Dynamics of the digital filter model is considered at the first time by using analytical and numerical methods. Existence and stability of fixed points are examined for all values of parameters. Low period cycles are found. With the aid of the Poincare map technique the 'maximal' attractor of the system is described for some regions of a parametrical plane. A separation of a parametrical plane into domains with qualitatively similar behavior of the system is constructed. Particularly, an existence of the specifically alternated 'tongues' and 'sausages' of cycles is shown. Domains of complex behavior are shown. Lyapunov exponents and fractal dimension of components of attractors are calculated for some values of parameters. Comparison with other models of filters is done.