Global MittagLeffler synchronization of fractionalorder delayed quaternionvalued neural networks: Direct quaternion approach Abstract   This paper investigates the global MittagLeffler synchronization (GMLS) issue for fractionalorder delayed quaternionvalued neural networks, which include leakage delays and transmission delays. First, a new lemma is established to estimate the Caputo fractional derivative for quaternion selfconjugate quadratic Lyapunov function, and a novel quaternionvalued linear feedback controller is designed. Then by utilizing quaternion matrix theory and our proposed lemma, some succinct GMLS criteria are derived respectively in quaternionvalued linear matrix inequality (LMI) form and complexvalued LMI form, which simplify and extend some previous work on the synchronization control for quaternionvalue neural networks. Finally, a numerical example is given to validate our theoretical results.

A new fixedtime stability theorem and its application to the fixedtime synchronization of neural networks Abstract   In this paper, we derive a new fixedtime stability theorem based on definite integral, variable substitution and some inequality techniques. The fixedtime stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixedtime stability theorems. Based on the new fixedtime stability theorem, the fixedtime synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixedtime synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixedtime synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixedtime stability theorems. What is more, the plaintext signals can be recovered according to the new fixedtime stability theorem, while the plaintext signals can not be recovered according to the existing fixedtime stability theorems.