content_image/324199.jpg
and omitting the first 500 iterations, we obtain the stroboscopic plot whose projection on the Y − Y$_{0}$ plane is shown in Figure 12. Since the plot is not placed on the line Y$_{0}$ = Y, we conclude that generalized synchronization does not occur in the couple A$_{2}$ − A$_{4}$. 

<img src='content_image/324199.jpg'>

It is worth noting that generalized synchronization does not take place also in the dynamics of the unidirectionally coupled subsystems B$_{1}$ and B$_{2}$, which are mentioned in Section 5, and this can be verified by means of the auxiliary system approach [1, 39] as well. 

## 7 The Global Unpredictability, Synergetics and Self-Organization 

The idea of the transition of chaos from one system to another, as well as the arrangement of chaos in an ordered way, can be viewed through the lens of self-organization [42, 65]. Durrenmatt [31] explained that “... a system is self-organizing if it acquires a spatial, temporal or functional structure without specific interference from the outside. By ‘specific’ we mean that the structure of functioning is not impressed on the system, but the system is acted upon from the outside in a nonspecific fashion." There are three approaches to self-organization, namely thermodynamic (dissipative structures), synergetic and the au- towaves approach. For the theory of dynamical systems (e.g. differential equations) the phenomenon means that an autonomous system of equations admits a regular and stable motion (periodic, quasiperi- odic, almost periodic). These are what are called autowaves processes [11] or self-excited oscillations [63] in the literature. We are inclined to add to the list one more phenomenon - chaos extension. For example, consider the collection of systems A$_{1}$, A$_{2}$, . . . , A$_{5}$ once again, where A$_{1}$ is the original generator of chaos. Because of the connections and the conditions discovered in our analysis, all the other subsys- tems, A$_{2}$, . . . , A$_{5}$, are also chaotic. We believe this is a self-organization phenomenon, that is, a coherent behavior of a large number of systems [42]. 

Haken [42], a German theoretical physicist, introduced a new interdisciplinary field of science, syner- getics, which deals with the origins and the evolution of spatiotemporal structures. Synergetics is based 

