Resumen de Dynamical systems applied to consciousness and brain rhythms in a neural network

Javier Alejandro Galadí García

• This thesis applies the great advances of modern dynamical systems theory (DST) to consciousness. Consciousness, or subjective experience, is faced here in two different ways: from the global dynamics of the human brain and from the integrated information theory (IIT), one of the currently most prestigious theories on consciousness.

  Before that, a study of a numerical simulation of a network of individual neurons justifies the use of the Lotka-Volterra model for neurons assemblies in both applications.

  All these proposals are developed following this scheme: • First, summarizing the structure, methods and goal of the thesis.

  • Second, introducing a general background in neuroscience and the global dynamics of the human brain to better understand those applications.

  • Third, conducting a study of a numerically simulated network of neurons. This network, which displays brain rhythms, can be employed, among other objectives, to justify the use of the Lotka-Volterra model for applications.

  • Fourth, summarizing concepts from the mathematical DST such as the global attractor and its informational structure, in addition to its particularization to a Lotka-Volterra system.

  • Fifth, introducing the new mathematical concepts of model transform and instantaneous parameters that allow the application of simple mathematical models such as Lotka-Volterra to complex empirical systems as the human brain.

  • Sixth, using the model transform, and specifically the Lotka-Volterra transform, to calculate global attractors and informational structures in global dynamics of the human brain.

  • Seventh, knowing the probably most prestigious theory on consciousness, the IIT developed by G. Tononi.

  • Eighth, using informational structures to develop a continuous version of IIT.

  • And ninth, establishing some final conclusions and commenting on new open questions from this work.

  The study of consciousness has started to grow into a mature science and the present thesis is a contribution to this growing body of work.

  This thesis brings a new perspective from the field of dynamical systems to the difficult problem of describing consciousness. In particular, it develops the use of Lotka-Volterra modelling of global attractors and informational structures for describing the dynamics of the human brain.

  The thesis is presented in a logical manner with nine chapters stating the background, methods, results and general conclusions.

  Of particular importance is the development of a novel framework of informational structures in a continuous version of the integrated information theory proposed by Tononi.

  Overall, the thesis is a contribution to our growing understanding of one of the central problems in neuroscience.