The Synchronization Process and Segmentation of Patterns in Complex Network

Abstract

The brain processes information with amazing speed. Neurons of different districts or even different cerebral hemispheres can reach synchronous firing almost simultaneously. The networks with local connections can not achieve such speed. The smallworld networks discussed widely recent years may be one of the choices. Our researches manifest that the small-world networks can reach the synchronous firing rapidly. We also demonstrate that the model has the basic functions of pattern segmentation and feature binding. The time delays and the noise are presented in the model. We also used the mechanism of stochastic resonance. 1．IntroductionThe observation of synchronous oscillation among neurons that are widely separated over the visual cortex suggest that the synchronization of neuronal activity play a functional role in information processing in the brain. It is believed that individual objects are represented by a larger number of neurons called a cell assembly. Neurons coding for the same object could be bound together by their synchronous firing, that means synchronous firing of neurons play important functional roles in feature binding and switching of cognitive states[1-6]. Since the finite speeds in information transmission in biological neural networks, It is necessary to consider the connection delays that determine this processing speeds.Watts and Strogatz [7] have shown that real networks of different nature have the small-world (SW) property, characterized by high clustering and the short average network distance between two nodes. The neural network of the worm Caenorhabditis elegans shares topological properties with this smallworld. Since then, many more of real-world networks have been identified to have the SW property. The human brain is a large, interacting, complex network with nontrivial topological properties. The characterization for the underlying architectures of such a network is an important issue in neuroscience. Small-world structure has been detected on the large scale using magneto-encephalography in the functional connectivity of brain areas , as well as on the small scale, in the anatomy of the visual cortex and the connectivity arising in cultured neuronal networks [8][9][10][11][12][13]. It is reported recently that significant short and long range connections were found in both intra and interhemispheric regions, many of which were consistent with known neuroanatomical pathways measured by human diffusion imaging, and the human brain anatomical network had robust small-world properties [14]. As the brain consists on all levels of many specialized and interacting regions, the efficiency of their interactions, both globally and locally is of crucial importance for almost any brain function. Small world networks, therefore, offer an optimal infrastructure for interactions within and between brain regions.Although synchronization has mainly been investigated so far using model neurons with simple connection topology, real neural networks have more complex structures. The mechanism of s...