Generating functionals for complex dynamical systems

生成泛函提供了从基本和容易理解的概念生成复杂和结构化的动力学的可能性。我们认为，生成泛函的使用可能导致复杂系统的更系统的表述和自由参数的数量的显著减少，即控制问题的降维。我们建议研究三个生成泛函的例子，一个能量泛函和两个基于多稳态优化和突触流量最小化的信息理论泛函。有趣的将是研究多稳态优化与由能量泛函产生的吸引子动力学之间的相互作用，一边是由能量泛函产生的吸引子动力学，另一边是由传入突触流量最小化产生的自限Hebbian学习规则。我们建议研究新的自组织过程的例子，特别是自适应波，由于潜在相图的内在适应而产生的自组织临界状态，以及自主更新神经网络中突触结构的形成。

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.