Dynamic Research On Several Types Of Delayed Complex-valued Neural Networks

Neural networks are computational systems inspired by the functions and dynamics of the human brain.They have been extensively researched and applied across various fields,including mathematics,computer science,physics,and biology.Real-valued neural networks(RVNNs)are a typical type of neural network that have been successfully applied to solve practical problems such as optimization computation,pattern recognition,economic forecasting,and machine fault diagnosis.Despite their success,RVNNs still have limitations in addressing certain practical problems,such as affine transformation and signal processing.Complex-valued neural networks(CVNNs)have emerged as a generalization of RVNNs and exhibit excellent performance in handling complex-valued information and addressing issues such as the exclusive OR(XOR)problem.These networks have been widely applied in various fields,such as temporal processing,optoelectronics,ultrasound imaging,and computer vision,where the dynamical behavior of CVNNs plays a crucial role in achieving effective performance.Hence,investigating the dynamical behavior of CVNNs are highly significant and relevant.In this thesis,we examine the dynamics of multiple types of time-lagged CVNNs,focusing on their global exponential stability and global exponential synchronization.The main research results include the following aspects:1.We investigated the synchronization and global exponential stability of a class of differential-algebraic neural networks with delay,assuming real and virtual separable activation functions.Using the differential-algebraic inequality and relevant properties of the nonsingular M-matrix,we derived a sufficient criterion for achieving global exponential stability in a complex-valued neural network with delay.Additionally,we designed an appropriate feedback controller and provided criteria to ensure global exponential synchronization between the drive and response systems.2.This thesis investigates the stability and synchronization of CVNNs with proportional delays and suppression factors,with a focus on their applications in secure communication.The proposed synchronization scheme ensures both finitetime and fixed-time synchronization of a class of inertial neural networks with multiple proportional delays.3.We consider the stability and synchronization problems of a class of delaybased Complex-Valued Neural Networks(CVNNs).Assuming that the activation function can be expressed as a combination of binary real and imaginary parts,we integrate the system into a differential-algebraic system and apply differentialalgebraic inequalities and tools to derive sufficient conditions for the stability and synchronization of the CVNNs.It is worth noting that this transformation can provide ideas and inspiration for the study of the dynamics of other types of delayed CVNNs.To verify the theoretical results obtained in this thesis,numerical simulations were conducted in each chapter using Matlab software.The simulations demonstrated the validity and reliability of the findings.On the one hand,the research results have improved the theoretical system of CVNNs to some extent.On the other hand,they offer theoretical support for the practical application of CVNNs in the fields of science and technology.