The book reviews the application of discrete fractional operators to biological, chemical reaction and chaotic system with applications in physics. The dynamical analysis is carried out using equilibrium points of the system for studying their stability properties and chaotic behavior are illustrated with the help of bifurcation diagrams and Lyapunov exponents.
The book is divided into three parts. Part I of the book deals with the application of discrete fractional operators in chemical reaction-based systems with biological significance. Two different chemical reaction models are analysed- one being disproportionation of glucose, which plays important role in human physiology and other constitutes the Lengyel – Epstein chemical model. Chaotic behavior of the systems is studied and the synchronization of the system is performed in this part of the book. Part II covers the analysis of biological systems like tumor immune system and neuronal models by introducing memristor based flux control. There are very few works carried out with flux controlled memristor elements in biological systems- this book provides a new direction towards the study. The memductance functions are considered as quadratic, periodic, and exponential functions. The final part of the book reviews the complex form of the Rabinovich-Fabrikant system which describes physical systems with strong nonlinearity exhibiting unusual behavior. This chapter will provide the study of the Rabinovich- Fabrikant system using discrete fractional operator. The book as a whole will provide a detailed understanding of the importance of constructing models with discrete fractional operators and change in dynamics between commensurate and incommensurate order systems.
Author Biography:
Vignesh Dhakshinamoorthyis an assistant professor in the department of Mathematics, School of Engineering and Technology, CMR University, Bangalore. Before joining CMR University, he was a Postdoctoral fellow of national defence University of Malaysia, Malaysia. His research interests include discrete fractional calculus, Chaos theory, and stability theory. He has published more than 50 research articles in national and international peer reviewed journals.
Guo-Cheng Wu has a B.S. degree in mathematics from Nantong University, Nantong, China, in 2005, the M.S. degree in mathematics from Shanghai University, Shanghai, China, in 2008, and the Ph.D. degree in fibrous materials physics from Donghua University, Shanghai, in 2011. He is currently the Dean and a Professor with the Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, China.,Dr. Wu has been serving as an Editorial Member for Applied Mathematics and Computation since 2017, Neural Computing and Applications since 2019, and Nonlinear Dynamics since 2021.
Santo Banerjee was working as Associate Professor, in the Institute for Mathematical Research (INSPEM), University Putra Malaysia, Malaysia till 2020, and also a founder member of the Malaysia-Italy Centre of Excellence in Mathematical Science, UPM, Malaysia. He is now associated with the Department of Mathematics, Politecnico di Torino, Italy. His research is mainly concerned with Nonlinear Dynamics, Chaos, Complexity and Secure Communication. He is a Managing Editor of The European Physical Journal Plus
