Controllability of Fractional-Order Directed Complex Networks, with Self Loop and Double Edge Structure
Hao Zhang, Diyi Chen, Beibei Xu, Rui Zhou · Journal of Circuits Systems and Computers · 2015
For that the conclusion of maximum matching is an important basic theory for controllability of complex networks, we first study the validity of maximum matching for fractional-order directed complex networks. We also develop a new analytical tool to study the controllability of an arbitrary fractional-order directed complex directed network with self loop by identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics. Through analyzing a mass of typical examples, we propose a new theory named “variant maximum matching” which is superior to the old one. Finally, we present some typical examples to prove the correctness of our conclusions.