Introduction to Mathematical Modeling and Chaotic Dynamics
Chapman and Hall/CRC – 2013 – 363 pages
Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB®.
The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural science, focusing on one- and two-dimensional continuous and discrete time models. Moving on to chaotic dynamics, the authors discuss ways to study chaos, types of chaos, and methods for detecting chaos. They also explore chaotic dynamics in single and multiple species systems. The text concludes with a brief discussion on models of mechanical systems and electronic circuits.
Suitable for advanced undergraduate and graduate students, this book provides a practical understanding of how the models are used in current natural science and engineering applications. Along with a variety of exercises and solved examples, the text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.
Introduction to Mathematical Modeling
What Is Mathematical Modeling?
Classification of Mathematical Models
Limitations Associated with Mathematical Modeling
A Modeling Diagram
Dynamic System and Its Mathematical Model
Numerical Tools and Software Used
Modeling of Systems from Natural Science
Models with Single Population
Two-Dimensional (2D) Continuous Models (Modeling of Population Dynamics of Two Interacting Species)
2D Discrete Models
Introduction to Chaotic Dynamics
Chaos and Chaotic Dynamics
Primary Routes to Study Chaos
Types of Chaos, Transients, and Attractors
Methods of Investigation for Detecting Chaos
Poincaré Map and Poincaré Section
Chaotic Dynamics in Model Systems from Natural Science
Chaos in Single Species Model Systems
Chaos in Two Species Model Systems
Chaos in Two Species Model Systems with Diffusion
Chaos in Multi-Species Model Systems
Modeling of Some Engineering Systems
Models in Mechanical Systems
Models in Electronic Circuits
Solutions to Odd-Numbered Problems
Exercises and References are included in each chapter.
Dr. Ranjit Kumar Upadhyay is a professor in the Department of Applied Mathematics at the Indian School of Mines. He has been teaching applied mathematics and mathematical modeling courses for more than 16 years. He is a member of the American Mathematical Society and the International Society of Computational Ecology, Hong Kong. His research areas include chaotic dynamics of real-world situations, population dynamics for marine and terrestrial ecosystems, disease dynamics, reaction–diffusion modeling, environmental modeling, differential equations, and dynamical systems theory.
Dr. Satteluri R.K. Iyengar is the dean of academic affairs and a professor of mathematics at Gokaraju Rangaraju Institute of Engineering & Technology. He was previously a professor and head of the Department of Mathematics at the Indian Institute of Technology New Delhi. He has been a professor for more than 22 years, has published numerous journal articles, and has been a recipient of several awards. His research areas encompass numerical analysis and mathematical modeling.