Dynamical Systems Analysis

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INTRODUCTION The human brain has a remarkable ability to manage the body functions, and process the information that allows us to act on a changeable external environment. To achieve these functions, during evolution, it developed a large computing power, and specialized functions, such as cognition, emotion and consciousness. With approximately 86 billion neurons (Herculano-Houzel, 2009), each neuron has approximately hundreds up to thousands of synapses, it has high structural complexity, and non-linearity, that endows with a rich dynamic.

It is also a physical system composed of neurons that communicate with each other through electrical discharges. With that in mind, it is no coincidence that the main model used in neuroscience to describe
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Another way to describe this fact is to say that these phenomena depend on the way the components of those systems are interconnected. In a complex network, such as the brain in addition to its large number of components, there are a variety of topologies that give rise to different complex dynamic patterns (Arenas et al.,2008). For the solution of binding problem, synchronization makes possible the emergence of new virtual neural assemblies in the brain, without creating permanent neural circuits. This suggestion received the support of various experiments carried out in animals, and humans. These experiments showed the presence of higher correlation between oscillations of neuron assemblies that represent the features of the object that gave rise to the stimulus. These studies also showed that depending on the oscillation frequency, synchronization has characteristic spatial range, specific brain areas, and links to different cognitive …show more content…
In recent years, several researches have been done where monitoring of neural synchronization activity was used as a tool to identify differences in the neural patterns between healthy subjects and others with mental disorders. These studies have shown that schizophrenia would rise due to the defective functional connections in networks generated through synchronization." (Uhlhaas, Roux, & Singer, 2013; Saalmann et al.,2012; Ronenwett & Csernansky, 2010) In particular, these studies have shown that synchronization in the beta frequency band in thalamocortical region was correlated with working memory. In addition, it was found that a reduction of the activity of mediodorsal thalamus and thalamus cortical areas leads to a deficiency in the processes of acquisition and maintenance of information. (Uhlhaas, Roux, & Singer, 2013).
Besides the beta frequency synchronization, synchronization of these studies showed correlation in the gamma band with schizophrenia (Spencer et al., 2004; 2008; 2009), (Uhlhaas et al. 2009; 2010) ,(Lee et al., 2003), (Wang et al.,

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