# Mathematical Modeling: With Applications in Physics, Biology, Chemistry, and Engineering

### Synopsis

Mathematical modeling helps us to understand the interaction between the components of biological and physical systems and prediction of the future of these models. Basically, building a mathematical and computational model needs to perform different experiments and obtain different data which depicts the evolution of system. These models transform all the information into a system of ordinary differential equations to do more analysis based on some mathematical useful tools and are flexible to analysis. Dynamic systems modeling has been frequently used to describe different biological and physical systems and has a very important role in predicting the interactions between multiple components of a system over time. A dynamical system describes the evolution of a system over time using a set of mathematical laws. Also, it can be used to predict the interactions between different components of a system. There are two main methods to model the dynamical behaviors of a system, continuous time modeling, discrete-time modeling. When the time between two measurements is negligible, the continuous time modeling governs the evolution of the system, however, when there is a gap between two measurements, discrete-time system modeling comes to play. Ordinary differential equations are the tool to model a continuous system and iterated maps represent the discrete generations.

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This book consists of five chapters:

- Chapter 1:
*Study on the Application of Stability Theory in Studying the Local Dynamics of Nonlinear Systems* - Chapter 2:
*Studying the Phenomenon of Neural Bursting and Spiking in Neurons: Morris-Lecar Model* - Chapter 3:
*Evaluating the Impact of Chloride Channel on Spiking Patterns of Morris-Lecar Model* - Chapter 4:
*An Overview: Global Sensitivity Analysis in Physiological Systems* - Chapter 5:
*A Detailed Study: Using Parametric Mathematical Modeling to Develop a Geometric and Topological Intuition for Molecular Knots*