Complexity of the Brain: Structure, Function and Dynamics

Abstract

It is often said in colloquial sense that the brain is a prototype of complex systems. A few different notions of complexity may have more formally related to neural systems. First, structural complexity appears in the arborization of the nerve terminals at the single neuron level, and in the complexity of the graph structure at network level. Second, functional complexity is associated to the set of tasks being performed by the neural system. Third, dynamic complexity can be identified with the different attractors of dynamic processes, such as point attractors, closed curves related to periodic orbits, and strange attractors expressing the presence of chaotic behavior. In the book with Michael Arbib, and John Szent´agothai [22] we tried to show that the understanding of the neural organization requires the integration of structural, functional and dynamic approaches. Structural studies investigate both the precise details of axonal and dendritic branching patterns of single neurons, and also global neural circuits of large brain regions. Functional approaches start from behavioral data and provide a (functional) decomposition of the system. Neurodynamic system theory offers a conceptual and mathematical framework for formulating both structure-driven bottom-up and function-driven top-down models.