Generating functionals for complex dynamical systems

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Generating functionals offer the possibility to generate complex and structured dynamics from basic and well understood concepts. We suggest that the use of generating functionals may lead to a more systematic formulation of complex systems and to a sizable reduction in the number of free parameters, viz to a dimensional reduction of the control problem. We propose to study three examples of generating functionals, an energy functional and two information theoretical functionals based on polyhomeostatic optimization and on synaptic flux minimisation. Of interest will be in particular to study the interaction between the polyhomeostatic optimization with the attractor dynamics generated by the energy functional, on one side, and, on the other side, with the self-limiting Hebbian learning rules resulting from the minimisation of the afferent synaptic flux. We propose to study instances of novel self-organizing processes, in particular adaptive waves, self-organized critical states resulting from the intrinsic adaption of the underlying phase diagram, and the formation of synaptic structures in autonomously updating neural networks.