Complex systems self-organization

Some Properties of Complex Systems Self-organization, the Butterfly Effect, Adaptability and Probabilistic Advantages... 

R. Feistel and W. Ebeling, Evolution of Complex Systems. Self-Organization, Entropy and Development (Kluwer, Boston, 1988). 

The criterion of the marginal complexity of self-organized systems... 

Another masterpiece of nature is self-organization of the tobacco virus, shown in Fig. 13.21. Such a complex system self-assembles because its parts not only fit one another (synthons), but also found themselves in solution and made perfect matching accompanied by an energy gain. Even more spectacular is the structure and functioning of bacteriophage T (Fig. 13.22). 

A recently described multicellular model that may offer promise is the formation of liver buds from pluripotent stem cells cultured with endothelial cells and mesenchymal stem cells (Takebe et al., 2013). This coculture system self-organizes into a 3D bud of cells with a complex vasculature and shows improved hepatic function compared to 2D controls. Despite this, the authors report a lack of biliary cell formation suggesting that this model, while being a step forward, requires independent reproduction and further development before fully recapturing the complex architecture of the liver. 

Thus, the increase in complexity of self-organized systems determines the increasing of order. 

The importance of numerical treatments, however, caimot be overemphasized in this context. Over the decades enonnous progress has been made in the numerical treatment of differential equations of complex gas-phase reactions [8, 70, 71], Complex reaction systems can also be seen in the context of nonlinear and self-organizing reactions, which are separate subjects in this encyclopedia (see chapter A3,14. chapter C3.6). 

Upon closer examination, we see that self-organization in complex system does not really violate the Second Law. The reason is that the Second Law requires a system to be isolated that is, it must not exchange energy or matter with its environment. 

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