Stability Analysis of Neural Networks

GRIENGGRAI RAJCHAKIT is Associate Professor at the Department of Mathematics, Faculty of Science, Maejo University, Chiangmai, Thailand. He received his Ph.D. in Applied Mathematics from the King Mongkut's University of Technology Thonburi, Bangkok, Thailand, on the topic of stability and control of neural networks. He received the Thailand Frontier Author Award by Thomson Reuters Web of Science (2016) and the TRF-OHEC-Scopus Researcher Award by The Thailand Research Fund, Office of the Higher Education Commission (OHEC) and Scopus (2016), respectively. His research interests are complex-valued neural networks, complex dynamical networks, control theory, stability analysis, sampled data control, multi-agent systems, and T-S fuzzy theory, and cryptography. He is a reviewer for various reputed journals and has authored and co-authored more than 111 research articles in various reputed journals.PRAVEEN AGARWAL is a Professor at theDepartment of Mathematics, Anand International College of Engineering, Jaipur, India. In 2006, he earned his Ph.D. in Mathematics from the Malviya National Institute of Technology, Jaipur, India. He has published over 250 articles related to special functions, fractional calculus, fixed point theory, mathematical modeling, and mathematical physics in several leading mathematics journals. His latest research has focused on partial differential equations, fixed point theory, neural networks, and fractional differential equations. On the editorial boards of several reputed journals, he has been involved in a number of conferences. Recently, he received the Most Outstanding Researcher 2018 Award for his contribution to mathematics by the Union Minister of Human Resource Development of India. He has received numerous international and national research grants. SRIRAMAN RAMALINGAM worked as Assistant Professor at the Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai, Tamil Nadu, India, from 2019 to 2020. He earned his Ph.D. from Thiruvalluvar University, Vellore, Tamil Nadu, India, in 2020. He His research interests are in dynamical systems theory include neural networks and time delay systems. He has authored and co-authored more than 20 research articles in various reputed journals and serves as a reviewer for various journals of repute.

“This book presents the foundations of stability analysis of neural networks in a well-organized manner. … This book will be very helpful to the research community working in the area of stability of dynamical systems, especially neural networks. Readers who are familiar with the basics of differential equations will find it very comfortable.” (Raju K. George, Mathematical Reviews, February, 2023)“The book … completes successfully the known lists of monograph dealing with neural networks. In fact any researcher or student dedicated to one of the topics tackled throughout the book should use it and for sure (s)he will be rewarded from the scientific point of view.” (Vladimir Răsvan, zbMATH 1485.93004, 2022)

• 1. Introduction.- 2. LMI-Based Stability Criteria for BAM Neural Networks.- 3. Exponential Stability Criteria for Uncertain Inertial BAM Neural Networks.- 4. Exponential Stability of Impulsive Cohen-Grossberg BAM Neural Networks.- 5. Exponential Stability of Recurrent Neural Networks with Impulsive and Stochastic Effects.- 6. Stability of Markovian Jumping Stochastic Impulsive Uncertain BAM Neural Networks.- 7. Global Robust Exponential Stability of Stochastic Neutral-Type Neural Networks.- 8. Exponential Stability of Discrete-Time Cellular Uncertain BAM Neural Networks.- 9. Exponential Stability of Discrete-Time Stochastic Impulsive BAM Neural Networks.- 10. Stability of Discrete-Time Stochastic Quaternion-Valued Neural Networks.- 11. Robust Finite-Time Passivity of Markovian Jump Discrete-Time BAM Neural Networks.- 12 Robust Stability of Discrete-Time Stochastic Genetic Regulatory Networks.