Global dissipativity and quasi-Mittag-Leffler synchronization of fractional-order complex-valued neural networks with time delays and discontinuous activations

This paper explores fractional-order complex-valued neural networks (FOCVNNs) with time delays and discontinuous activation functions. A novel fractional-order inequality is utilized to study this system as a whole without dividing it into different components in the complex plane. Firstly, the existence of global Filippov solutions in the complex domain is proven by using the theories of vector norms and fractional calculus. Next, some sufficient conditions are derived to ensure the global dissipativity and quasi-Mittag-Leffler synchronization of FOCVNNs through the use of nonsmooth analysis and differential inclusion theory. The error bounds of quasi-Mittag-Leffler synchronization are also estimated without relying on the initial values. Finally, some numerical simulations are conducted to demonstrate the effectiveness of the presented findings.