Introduction to Mathematical Modeling and Chaotic Dynamics

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.