Chaotic Dynamics of Fractional Discrete Time Systems

Cover
Title Page
Copyright Page
Preface
Table of Contents
1. Mathematical Perspective of Real World Models
	1.1 Mathematical Modelling
	1.2 History of Fractional Calculus
	1.3 Discrete Fractional Calculus
	1.4 Chaotic Systems
	1.5 Summary
2. Chaos and Synchronization of Fractional Order Discrete–Time Chemical Reaction Systems
	2.1 Modelling in Chemistry
	2.2 Chemical Reaction Systems
	2.3 Chaotic Dynamics of Lengyel-Epstein Model
	2.4 Chaotic Dynamics of Enzyme and Substrate Mechanism Model
	2.5 Synchronization
	2.6 Summary
3. Chaos in Discrete–Time Fractional Order Bio-Chemical Models
	3.1 Introduction
	3.2 Mathematical Models of Bio-Chemical Reactions
	3.3 Chaos in Commensurate Order Systems
	3.4 Chaos in Incommensurate Order Systems
	3.5 Synchronization of Bio-Chemical Models
	3.6 Summary
4. Dynamical Analysis of Memristor Based KTZ Neuron Model with Fractional Difference Operator
	4.1 Introduction
	4.2 Mathematical Models of Neuron
	4.3 Memristor Based KTZ Neuron Model
	4.4 Summary
5. Discrete Fractional Model of Tumor and Effector Cells Interaction with Chemotherapy
	5.1 Introduction
	5.2 Mathematical Models of Tumor-Immune System
	5.3 Commensurate Order System
	5.4 Tumor and Effector Cells Interaction Model with Incommensurate Order
	5.5 Tumor Immune Model with Chemotherapy
	5.6 Summary
6. Attractors in Fractional Order Discrete–Time Rabinovich-Fabrikant System
	6.1 Nonlinearity in Nature
	6.2 Rabinovich–Fabrikant System
	6.3 Equilibrium Points and Stability
	6.4 Bifurcation Analysis
	6.5 Complex Rabinovich–Fabrikant System
	6.6 Incommensurate Order Complex Rabinovich–Fabrikant System
	6.7 Summary
7. Dynamical Analysis of Variable Order Discrete–Time Plasma Perturbation Model
	7.1 Introduction
	7.2 Plasma Perturbation Model (PPM)
	7.3 Commensurate Order PPM Model
	7.4 Incommensurate Order PPM Model
	7.5 Dynamics of the Plasma Perturbation Model for Variable Order
	7.6 Summary
Index