"In this book, authors would like to investigate the application of discrete fractional operators to biological, chemical reaction and chaotic system with applications in physics. The dynamical analysis will be carried out using the equilibrium points ofthe system for studying their stability properties and chaotic behavior will be illustrated with the help of bifurcation diagrams and Lyapunov exponents. The book is divided into three parts. Part - I is dedicated for the analysis of biological systems like tumor immune system and neuronal models with introducing memristor based flux control. There are very few works carried out with flux controlled memristor elements in biological systems, we in this book would like to provide new direction towards the study. The memductance functions are considered as quadratic, periodic, exponential functions. Part - II of the books depicts the application of discrete fractional operators in chemical reaction-based systems with biological significance. Here, we perform analysis of two different chemical reaction models 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. For the final part of the book, we propose 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 chaotification technique and the application of the systems will be explored in the final chapter. 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"--
The book reviews the application of discrete fractional operators to biological, chemical reaction and chaotic system with applications in physics.
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.
Mathematical Perspective of Real World Models. Chaos and Synchronization
of Fractional Order DiscreteTime Chemical Reaction Systems. Chaos in
DiscreteTime Fractional Order Bio-Chemical Models. Dynamical Analysis of
Memristor Based KTZ Neuron Model with Fractional Difference Operator.
Discrete Fractional Model of Tumor and Effector Cells Interaction with
Chemotherapy. Attractors in Fractional Order DiscreteTime
Rabinovich-Fabrikant System. Dynamical Analysis of Variable Order
DiscreteTime Plasma Perturbation Model.
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.
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