Mathematical Modeling: Models, Analysis and Applications

Content: 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