Synchronization transitions on complex thermo-sensitive neuron networks with time delays.

We have numerically studied the firing synchronization transitions on random thermo-sensitive neuron networks in dependence on information transmission delay tau, network randomness p, and coupling strength g. It is found that as tau is increased the neurons can exhibit transitions from burst synchronization (BS) to clustering anti-phase synchronization (APS), and further to spike synchronization (SS). It is also found that, with increasing p or g, there are transitions from spatiotemporal chaos to BS, then to APS, and finally to SS. However, the APS state with p or g exists only for intermediate tau values within a narrow range. For tau values outside this range, the APS state does not appear and the firings change directly from spatiotemporal chaos to BS or SS. These results show that, as time delay can do, network topology and coupling strength can also cause complex synchronization transitions in the neurons. In particular, the novel phenomenon of APS state with p or g shows that, with the help of appropriate random connections or coupling strength, the neurons may exhibit the APS behavior at a certain time delay for which the APS does not appear originally. These findings imply that time delay, network randomness, and coupling strength may have subtle effects on the firing behaviors on neuronal networks, and thus could play important roles in the information processing in neural systems.