Chaotic Dynamics of Fractional Discrete Time Systems

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.