Synchronization in fixed/preassigned-time of delayed fully quaternion-valued memristive neural networks via non-separation method

This paper mainly centers on investigating issues of synchronization of delayed memristive quaternion-valued neural networks (MQVNNs), which are first studied with an unconventional non-separation approach for the fully quaternion-valued (QV) parameters (i.e. state vectors, weights, inputs and outputs). First, QV sign function and norms are introduced and new properties of quaternions are established, which are the basis of the non-separation approach. Next, more relaxed conditions with a new pure lemma are explored to guarantee fixed-time (FXT) or preassigned-time (PST) synchronization and the settling times (STs) are measured. Specially, the ST of PST synchronization is pre-specified and irrelevant to any parameter of the systems or controllers, which is more independent. Subsequently, controller strategies are given to realize FXT and PST synchronization of the discussed systems. Lastly, the effectiveness and superiority of the achieved theoretical results are illustrated by numerical examples.