Dynamical Behavior in a DPCM System with an Order 2 Predictor. Case of a Constant Input

Abstract

This paper deals with a differential pulse code modulation (DPCM) transmission system. It includes an encoder which uses a coupling between a transversal predictor and a nonlinear quantizer. This paper studies, from a dynamical point of view, an order 2 DPCM system modeled via a noninvertible two-dimensional map. Chaotic phenomena can be observed; depending on the kind of application, it can be interesting to avoid chaos or to use it. In both cases, it is necessary to understand the mechanisms which give rise to it. For that, the usual tools of chaotic dynamics are used (bifurcation structures, critical and invariant manifolds).

Invariant Curves of Quadratic Maps of the Plane from the One-Parameter Family Containing the Trace Map

“…After this µ-value, the annular chaotic attractor becomes a one piece chaotic attractor (CA). This situation has already been obtained in [29], [19]. In all above cases the basins of attraction of CIC, WCR, ACA or CA have interior points, and CIC, WCR, ACA and CA are connected sets.…”

“…The chaotic attractor disappears [29], [19]. As it follows from [12], the invariant triangle ∆ 2 is not an attractor of F 2 .…”