Generating functionals for complex dynamical systems

复杂动力系统的生成函数

• 批准号: 241883649
• 负责人: Professor Dr. Claudius Gros
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/241883649?language=en
• 关键词: Generating; functionals; complex; dynamical; systems

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.

生成函数提供了从基本和易于理解的概念生成复杂和结构化动态的可能性。我们认为，生成泛函的使用可能会导致复杂系统的更系统的表述，并导致自由参数数量的大量减少，即控制问题的维数减少。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通量最小化的信息理论泛函。我们特别感兴趣的是研究多稳态优化与能量泛函产生的吸引子动力学之间的相互作用，以及另一方面，由传入突触通量最小化产生的自限制Hebbian学习规则之间的相互作用。我们建议研究新的自组织过程的实例，特别是自适应波，由底层相图的内在适应引起的自组织临界状态，以及自主更新神经网络中突触结构的形成。