One of the most effective methods for comprehending,
evaluating, and forecasting the behaviour of real-world systems that arise in
the fields of science, engineering, biology, economics, and the social sciences
is mathematical modelling. Models give researchers a methodical framework for
investigating system dynamics, testing theories, and directing decision-making
by converting physical, biological, or socioeconomic processes into
mathematical language.
The goal of this book is to present a thorough, organised,
and understandable introduction to mathematical modelling based on continuous
dynamical systems, with a focus on ordinary differential equations. The
presentation integrates theoretical foundations, qualitative analysis, and
computational tools, allowing readers to transition seamlessly from model
creation to analytical insight and numerical exploration.
The introductory chapters present essential ideas of
mathematical modelling, encompassing modelling assumptions, variable selection,
parameter interpretation, and dimensional consistency. Continuous first-order
differential equations are formulated using compelling examples from natural
and applied sciences, thus building a robust conceptual foundation.
The qualitative theory of dynamical systems, including
linearization, equilibrium analysis, and stability theory, is the main topic of
the following chapters. These methods make it possible to comprehend the
behaviour of long-term systems without depending on explicit solutions, which
are frequently not available for nonlinear models.
Then, bifurcation theory is introduced to show how qualitative
changes in system dynamics can result from minor changes in parameters. In
applied models, bifurcations that are often encountered are given particular
consideration. Biological, ecological, and engineering systems are used to
illustrate the analytical and geometric methods for identifying and
characterizing periodic solutions that are developed in the limit cycles
chapter.
The final chapter is dedicated to simulation techniques,
acknowledging the essential role of computation in contemporary modelling.
Numerical approaches, phase-plane simulations, and computational tools like
MATLAB are employed to enhance analytical findings and to explore intricate
systems that exceed closed-form analysis.
This book is designed for advanced undergraduate and graduate
students, along with academics and practitioners pursuing a comprehensive
introduction to mathematical modelling and dynamical systems. The information
is appropriate for courses in applied mathematics, mathematical biology,
engineering mathematics, and associated fields. The literature reinforces
theory using examples, pictures, and simulations to enhance intuition and
practical comprehension.
It is intended that this book will give readers the
mathematical rigour and modelling understanding they need to examine real-world
occurrences and create insightful models for a variety of application domains
Author(s) Details
Dr. K. Ramesh
Anurag University, Hyderabad, Telangana, India.
Dr. G. Ranjith Kumar
Anurag University, Hyderabad, Telangana, India.
Dr. K. Lakshmi
Narayan
Department of Humanities & Sciences, VJIT, Hyderabad, Telangana, India.
Dr. A. V. Papa Rao
Department of Mathematics, JNTU-GV College of Engineering, Vizianagaram,
Andhra Pradesh, India.
Please see the link:- https://doi.org/10.9734/bpi/mono/978-81-69006-52-1
