Self-organisation of complex dynamical systems: from synergetics to neuromorphic systems.

The intuitive idea of self-organisation in complex dynamical systems is that global patterns and structures emerge from locally interacting elements like atoms in laser beams, molecules in chemical reactions, proteins in cells, cells in organs, neurons in brains, agents in markets, etc. Hermann Haken introduced a mathematically precise and rigorous formalism of synergetics. In this framework we define local activity as the cause of self-organizing complexity which can be tested in an explicit and constructive manner. This principle of local activity can also be defined in the theory of nonlinear electronic circuits. It is not restricted to a certain domain, but can be generalized and proven for the class of nonlinear reaction-diffusion systems in physics, chemistry, biology, and brain research. An example is an improved Hodgkin-Huxley axon circuit model of the brain as network of physiology. It turns out that neuromorphic computing approximates the energetic efficiency of human brains and avoids the enormous increase of energy consumption with traditional digital computing. Obviously, traditional digitalization is closely connected with one of the most challenging problems of mankind-the increasing demand for energy with all its consequences for environmental and climate problems. Thus, synergetics with the local activity principle strongly supports the request for sustainable computing inspired by network physiology.