Mathematical modeling Models, Analysis and Applications

This how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB^®, Mathematica^®, and MatCont are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project.

About Mathematical Modeling
What Is Mathematical Modeling?
History of Mathematical Modeling
Latest Development in Mathematical Modeling
Various Functional Forms in Mathematical Modeling
Merits and Demerits in Mathematical Modeling

Mathematically Modeling Discrete Process
Difference Equations
Introduction to Discrete Models
One Dimensional Density Independent Models
One Dimensional Density Dependent Models
Stability Analysis
Nonlinear Two-Dimensional Models: Stability and Bifurcation

Continuous Models Using Ordinary Differential Equations
Introduction to Continuous Models
Formation of Various Continuous Models
Steady State Solutions
Stability and Linearization
Phase Plane Diagrams of Linear Systems
Stability Characteristics
Null Cline Approach
Poincare Bendixson Theory
Bifurcation and Limit Cycle

Spatial Models Using Partial Differential Equations
Diffusion Equations: Observations and Consequences
Dispersal Models Using Diffusion
Effect of Density Dependent Dispersal on Population Dynamics
Models for Age Dependent Dispersal
Steady State Solutions and Traveling Waves
Non Linear Stability Analysis for Diffusion Reaction System
Bifurcation Analysis and Limit Cycles
Numerical Solutions of Differential Equations with Diffusion
Pattern Developing Instability in Diffusion Reaction Systems
Effect of Cross Diffusion

Modeling with Delay Differential Equations
An Introduction to Delay Differential Equations
Various Mathematical Models with Time Delay
Delay Induced Model for Tumor Immune Interaction (Single Discrete Delay)
Stage Structure Predator Prey Models with Multiple Delays and Its Global Stability
Models with Distributed Delays

Modeling with Stochastic Differential Equations
Stochastic Process and Stochastic Differential Equations: a Preview
Effect of Additive Noise on a Logistic Equation
Stochastic Stability: Asymptotically Mean Square Stable
Mean Square Stability of a Stochastic Model with Time Delays
Numerical Simulation of Stochastic Differential Equations
Stochastic Metapopulation Models

Examples and Exercises appear at the end of each chapter.