Synchronization Analysis of Complex-Valued Artificial Neural Networks with Distributed Delays in Medical Image Processing

Machine Learning is a fundamental subfield of artificial intelligence that focuses on analyzing and interpreting patterns and structures in data. In addition, artificial neural networks (ANNs) are a powerful tool for machine learning because they can be trained to recognize patterns in data, and they can be used to make predictions about new data. In comparison to conventional real-valued artificial neural networks (RVANNs), complex-valued artificial neural networks (CVANNs) are capable of making more accurate predictions because they have input and output signals and parameters such as weights and thresholds which are all complex numbers. It has been demonstrated that ANNs are capable of significantly improving the accuracy and efficiency of medical image analysis, thereby improving the quality of diagnosis and treatment. There is no doubt that all those applications of CVANNs are highly dependent of their nature of dynamics. Therefore, we are focusing in this study on the problem of solving the global exponential synchronization problem of master-slave CVANNs with distributed delays and the matrix measure method (MMM). In this case, the distributed time-varying delay is not subject to any derivative constraints. We first decompose the original CVANNs into equivalent RVANNs, which avoids the complexity of complex numbers. Therefore, the synchronization problem of CVANNs is analyzed by studying their equivalent RVANNs. Then, using Lyapunov function, Halanay inequality and MMM, some new delay-dependent sufficient conditions for the global exponential synchronization of the error systems with designed control are derived by separating CVANNs into real and imaginary parts. The results obtained in this study are novel and that are easy to verify and implement. Moreover, the results provides a new insights into the global exponential synchronization of master-slave CVANNs. Finally, a numerical illustration is presented with their simulations to illustrate the effectiveness of the obtained theocratical analysis.