Fixed-time synchronization of delayed multiplex networks with impulsive effects

The fixed-time synchronization of delayed multiplex networks with impulsive effects is studied. The delayed topology of a multiplex network is considered, which contains both interlayer and intra-layer relationships. We thoroughly investigate two distinct impulses, involving synchronizing and desynchronizing impulses, respectively. Besides, we design the adaptive controller to drive the given networks with distinct impulsive effects into fixed-time synchronization. Emphatically, the designed controller has no bearing on any sign functions, and as a result, it eliminates the chattering phenomena that appear in many results from previous research. In addition, sufficient conditions to reach fixed-time synchronization are given under synchronizing and desynchronizing impulses correspondingly. Ultimately, coupled single-link robot arms are chosen as the application of our theoretical findings, and a few illustrative examples are exhibited to present the effectiveness.