4 research outputs found
Dynamical systems applied to consciousness and brain rhythms in a neural network
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.
These nine points of this scheme correspond to the nine chapters of this thesis
Model transform and local parameters. Application to instantaneous attractors
The model transform fits exactly the parameters of a suitable model to empirical or simulated data in each point in time and/or space. We describe several examples of concrete model transforms and their applications. The model transform allows simple theoretical models to be applied to complex empirical systems in each short interval of time or/and in each local neighborhood. The model can be chosen to identify, for instance, the temporal evolution of the attractor landscape for empirical systems which depict a complex dynamics over time
Informational structures: A dynamical system approach for integrated information
Integrated Information Theory (IIT) has become nowadays the most sensible general theory of consciousness. In addition to very important statements, it opens the door for an abstract (mathematical) formulation of the theory. Given a mechanism in a particular state, IIT identifies a conscious experience with a conceptual structure, an informational object which exists, is composed of identified parts, is informative, integrated and maximally irreducible. This paper introduces a space-time continuous version of the concept of integrated information. To this aim, a graph and a dynamical systems treatment is used to define, for a given mechanism in a state for which a dynamics is settled, an Informational Structure, which is associated to the global attractor at each time of the system. By definition, the informational structure determines all the past and future behavior of the system, possesses an informational nature and, moreover, enriches all the points of the phase space with cause-effect
power by means of its associated Informational Field. A detailed description of its inner structure by invariants and connections between them allows to associate a transition probability matrix to each informational structure and to develop a measure for the level of integrated information of the system.Ministerio de Economía, Industria y CompetitividadJunta de AndalucíaFondo Europeo de Desarrollo Regiona
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