Generalized synchronization in discrete maps. New point of view on weak and strong synchronization

TL;DR

This paper refines the understanding of generalized synchronization in discrete maps by emphasizing the importance of prehistory and extending the phase tube approach, leading to a reconsideration of weak and strong synchronization distinctions.

Contribution

It introduces a refined perspective on generalized synchronization in discrete maps, incorporating prehistory and extending the phase tube method for coupled systems.

Findings

Prehistory is essential in analyzing generalized synchronization.

The phase tube approach is extended to discrete-time coupled systems.

The division between weak and strong synchronization needs reevaluation.

Abstract

In the present Letter we show that the concept of the generalized synchronization regime in discrete maps needs refining in the same way as it has been done for the flow systems [PRE, 84 (2011) 037201]. We have shown that\alkor{, in the general case, when the relationship between state vectors of the interacting chaotic maps are considered,} the prehistory must be taken into account. We extend the phase tube approach to the systems with a discrete time coupled both unidirectionally and mutually and analyze the essence of the generalized synchronization by means of this technique. Obtained results show that the division of the generalized synchronization into the weak and the strong ones also must be reconsidered. Unidirectionally coupled logistic maps and H\'enon maps coupled mutually are used as sample systems.