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Full Description
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.
Contents
Mathematical Perspective of Real World Models. Chaos and Synchronization of Fractional Order Discrete-Time Chemical Reaction Systems. Chaos in Discrete-Time 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 Discrete-Time Rabinovich-Fabrikant System. Dynamical Analysis of Variable Order Discrete-Time Plasma Perturbation Model.
