Synchronization of linearly coupled reaction-diffusion neural networks with hybrid coupling and time-varying delays via aperiodically intermittent pinning control [article]

Xiwei Liu, Zhang Chen, Lingjun Zhou
2016 arXiv   pre-print
In this paper, the complete synchronization problem of linearly coupled neural networks with reaction-diffusion terms and time-varying delays via aperiodically intermittent pinning control is investigated. The coupling matrix for the network can be asymmetric. Compared with state coupling in the synchronization literature, we design a novel distributed coupling protocol by using the reaction-diffusion coupling-spatial coupling, which can accelerate the synchronization process. This can be
more » ... ed as the main difference between this paper and previous works. Using the Lyapunov function and theories in the aperiodically intermittent control, we present some criteria for the complete synchronization with a static coupling strength. In this case, there is no constraint on the bound of time-varying delays, so it can be larger than the length of control span. On the other hand, for the network with an adaptive coupling strength, we propose a simple adaptive rule for the coupling strength and prove its effectiveness rigorously. In this case, the bound of time-varying delay is required to be less than the infimum of the control time span. Finally, numerical simulations are given to verify the theoretical results.
arXiv:1604.03379v1 fatcat:zqeglcs3mrg63kdpcm3cwnxwy4