Chaotic Communication with a Time Delayed Map

Owing to their rich dynamical structures, chaotic systems show great potential for the design and employment of chaotic communication devices. The basic idea is that the underlying attractors and repellors of the chaotic system can be used as natural guides for information through suitable intervention in its dynamics (see e.g. Farmer [1], Carroll [2] and Hayes [3] and references therein). Coupled map lattices, the class of chaotic systems investigated here, have been studied extensively since the mid eighties due to their fascinating phenomenology and their suitability as simple yet high dimensional chaotic paradigms (see e.g. Kaneko [4] or [5, 6] and references therein), and their dynamics is thus reasonably well known. In this letter, the special properties of one of the universality classes of the diffusively coupled logistic map, the frozen random pattern, will be exploited for encoding digital information in novel way by combining it with a newly introduced shifted form of the diffusively coupled logistic time-delayed map. The standard diffusively coupled map lattice, due to its spatial nature, would only be suitable for generating an encoded signal in chunks of its system size. While possible, this would be rather awkward since not only the signal would need to be buffered carefully, clear demarcaters that indicate the start and end of a chunk would also be necessary. In order to obtain a more efficient continuous procedure, rather than employing the coupled map lattice itself, the phenomenologically equivalent time delayed map [7] was chosen as the basis for the communications method. It is defined as: xn = (1 ε) f (xn N)+ ε 2 ( f (xn N 1)+ f (xn N+1)) ; (1)