Chimera states of neuron networks with adaptive coupling

To better understand the diversity of dynamical patterns in the brain network of cerebral cortex, we study the collective behaviors of coupled neurons in complex networks with adaptive coupling. Based on the mutual interaction between dynamics and coupling strength in neuron systems, we let the coupling matrix evolve with the dynamics of neurons. We find that with suitable phase parameters, the coupling matrix will be self-organized into stabilized states and chimera states will be induced. The patterns of these chimera states may be different and abundant, depending on the different network topologies such as the fully connected, random, and scale-free networks. In particular, we apply this adaptive model to the realistic network of cerebral cortex and interestingly find that the adaptive coupling can also induce a diversity of chimera states, which may provide a new insight for the high capability of flexible brain functions. Moreover, we find that the preference of observing chimera states in heterogeneous networks is greater than that in homogeneous networks, and the latter is greater than that in the fully connected network, which may be one of the reasons for the nature to choose the specific sparse and heterogeneous structure of our brain network.