Chaotic Dynamics of Fractional Discrete Time Systems

The book reviews the application of discrete fractional operators in diverse fields such as biological and chemical reactions, as well as chaotic systems, demonstrating their applications in physics. The dynamical analysis is carried out using equilibrium points of the system for studying their stability properties and the chaotic behaviors are illustrated with the help of bifurcation diagrams and Lyapunov exponents.

The book is divided into three parts. Part I 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 an important role in human physiology and the other is the Lengyel – Epstein chemical model. Chaotic behavior of the systems is studied and the synchronization of the system is performed. Part II covers the analysis of biological systems like tumor immune system and neuronal models by introducing memristor based flux control. 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.

Vignesh Dhakshinamoorthy is an assistant professor in the Department of Mathematics, CMR University, Bangalore. Before joining CMR University, he was a Postdoctoral fellow of the 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 (2005), a M.S. degree in mathematics from Shanghai University, Shanghai, China (2008), and a Ph.D. in fibrous materials physics from Donghua University, Shanghai (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 is an Editorial Member for Applied Mathematics and Computation, Neural Computing and Applications, and Nonlinear Dynamics.

Santo Banerjee was an 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 the Managing Editor of The European Physical Journal Plus.