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 (R).
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.
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.
Introduction to Mathematical Modeling Introduction What Is Mathematical Modeling? Classification of Mathematical Models Limitations Associated with Mathematical Modeling Modeling Approaches Modeling/Cyclic Processes A Modeling Diagram Compartment Models Mathematical Preliminaries Dynamic System and Its Mathematical Model Numerical Tools and Software Used Modeling of Systems from Natural Science Introduction Models with Single Population Two-Dimensional (2D) Continuous Models (Modeling of Population Dynamics of Two Interacting Species) 2D Discrete Models Introduction to Chaotic Dynamics Introduction Chaos and Chaotic Dynamics Primary Routes to Study Chaos Types of Chaos, Transients, and Attractors Methods of Investigation for Detecting Chaos Poincare Map and Poincare Section Lyapunov Exponents Chaotic Dynamics in Model Systems from Natural Science Introduction 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 Introduction Models in Mechanical Systems Models in Electronic Circuits Nonlinear Circuits Solutions to Odd-Numbered Problems Index Exercises and References are included in each chapter.