Estimating and adjusting abnormal networks with unknown parameters and topology

The changes of parameters and topology in a complex network often lead to unexpected accidents in complex systems, such as diseases in neural systems and unexpected current in circuit system, so the methods of adjusting the abnormal network back to its normal conditions are necessary to avoid these problems. However, it is not easy to detect the structures and information of each network, even if we can find a network which has the same function as the abnormal network, it is still hard to use it as a reference to adjust the abnormal network because a lot of network information is unknown. In this paper, we design a "bridging network" as an information bridge between a normal network and an abnormal network to estimate and control the abnormal network. Through the "bridging network" and some adaptive laws, the abnormal parameters and connections in abnormal network can be adjusted to the same conditions as those of the normal network which is chosen as a reference model. Finally, the "bridging network" and the abnormal network achieve synchronization with the normal network. Besides, the detailed inner information in normal network and abnormal network can be accurately estimated by this "bridging network." Finally, the nodes in the abnormal network will behave normally after the correction. In this paper, we use Hindmarsh-Rose model as an example to describe our method.