The stationarity control of the average links for the Hebb complex dynamical network via external stimulus signals

The model of complex dynamical network (CDN) can be represented as the mathematic graph, in which some characteristics may emerge from the dynamic nodes group (NG) and links group (LG). This paper primarily focuses on the feature appearing from the dynamic links. The average link weight (ALW), as a novel quantitative index to describe the characteristic of dynamic links is introduced. Inspired by the Hebb’s neuroscience theory, the Hebb complex dynamical network (HCDN) is constructed. The ALW of the HCDN can track a given target via external stimulus signals with adaptive amplifiers’ proportional coefficients. In other words, the stationary network implies the ALW is a constant in time. Finally, two simulation examples are performed to validate the proposed adaptive update law’s effectiveness. •The index of the average values-weighted of the links (ALW) is constructed by using Hebb’s neural theory, which is novel.•We introduce the ALW in place of the mean value to describe the overall change of links weights among many nodes in time. In addition, the stationary network implies the ALW is a constant in time, which is novel.•Using the principle of amplifiers, the ALW of Hebb complex dynamical network (HCDN) is controlled by adjusting the adaptive update law of the amplifier’s proportional coefficients to track a given reference signal.