Formation Of Small-World Network Containing Module Networks In Globally And Locally Coupled Map System With Changes In Global Connection With Time Delay Effects

In this study, we performed comprehensive morphological investigations of spontaneously formed network structures among elements in coupled map systems involving global connections that change depending on the synchronicity of states of elements and spatially local connections. The model formed various hierarchical networks, some of which were classified as small-world networks containing multiple module networks, similar to the neural network of mammalian brains. Moreover, such complex networks were formed in wider parameter regions when the global connection to an element from the other element was strengthened by the synchronization between the present and past states of the former and latter elements, respectively. This study suggests that the time delay effects for connection changed among elements and local interactions promoted the self-organization of small-world networks containing module networks, such as neural networks; neural networks contain them as spike-timing-dependent plasticity and inter-neuron interaction through glial cells.