  This paper analyses the behaviour of a second order DPCM (Differential Pulse
Code Modulation) transmission system when the nonlinear characteristic of the
quantizer is taken into consideration. In this way, qualitatively new
properties of the DPCM system have been unravelled, which cannot be observed
and explained if the nonlinearity of the quantizer is neglected. For the
purposes of this study, a piece-wise linear nondifferentiable quantizer
characteristic is considered. The resulting model of the DPCM is of the form of
iteration equations (i.e. map), where the inverse iterate is not unique (i.e.
noninvertible map). Therefore the mathematical theory of noninvertible maps is
particularly suitable for this analysis, together with the more classic tools
of Non Linear Dynamics. This study allowed us in addition to show from a
theoretical point of view some new properties of nondifferentiable maps, in
comparison with differentiable ones. After a short review of noninvertible
maps, the presented methods and tools for noninvertible maps are applied to the
DPCM system. An original algorithm for calculation of bifurcation curves for
the DPCM map is proposed. Via the studies in the parameter and phase plane,
different nonlinear phenomena such as the overlapping of bifurcation curves
causing multistability, chaotic behaviour, or multiple basins with fractal
boundary are pointed out. All observed phenomena show a very complex dynamical
behaviour even in the constant input signal case, discussed here.
