Multi-Type Synchronization for Second-Order Memristive Neural Networks with Mixed Time-Varying Delays

作者：Wang, Xiulei; Jian, Jigui^*

来源：NEURAL PROCESSING LETTERS, 2023, 55(2): 1759-1781.

DOI：10.1007/s11063-022-10962-y

• Second-order neural network
• Memristor
• Adaptive control
• Feedback control
• Synchronization
• Mixed time-varying delay

Without changing the original systems into the usual first-order ones, this article focuses on the finite-time synchronization (Fin-TS), global exponential synchronization (GES) and fixed-time synchronization (Fix-TS) of second-order memristive neural networks (SMNNs) with mixed time-varying delays. According to Lyapunov functional method, inequality techniques and contriving adaptive control and feedback control strategies with a power exponent, some algebraic criteria are simultaneously derived to ensure the Fin-TS, GES and Fix-TS of the concerned SMNNs by adjusting the control gain parameters and the power exponent in the controllers. The obtained sufficient conditions are simple and easy to verify. Different from existing ones, the Fin-TS, GES and Fix-TS are straightway analyzed via accepting some new Lyapunov functionals with the state variables and the derivative of the state variables. Besides, the settling time (ST) of the Fin-TS and Fix-TS and the exponential convergence rate of the GES are also estimated. Ultimately, a numerical example is given to prove the validity of the theoretical results.