Effect analysis of pinning and impulsive selection for finite-time synchronization of delayed complex-valued neural networks

We explored the phenomenon of finite-time synchronization for coupled complex-valued neural networks that were subject to mixed-variable delays. To address this challenge, an impulsive pinning control strategy was proposed. The method presented entailed the dynamic adjustment of specific nodes at distinct impulsive intervals, contingent upon the magnitude of the errors observed in those nodes. Furthermore, an enhanced technique utilizing the sign function was employed to simultaneously manage the real and imaginary components of the complex-valued neural networks. By applying finite-time stability theorems and utilizing complex-valued inequalities, sufficient conditions for achieving finite-time synchronization and determining stability time under the influence of delayed impulsive effects were established. A comprehensive discussion on the interaction between impulsive effects and pinning strategies was also included. It was noted that integrating impulsive effects with pinning ratios enabled precise control over nodes exhibiting significant errors, thereby promoting rapid convergence within finite time frames. Our findings highlight the effectiveness of impulsive pinning control in enhancing synchronization stability, providing significant insights into the practical applications of complex-valued neural networks, particularly in image processing.