ISBN 978-93-91312-16-9 (Print)
ISBN 978-93-91312-24-4 (eBook)
DOI: 10.9734/bpi/mono/978-93-91312-16-9

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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Mathematical Modeling: With Applications in Physics, Biology, Chemistry, and Engineering, Edition-2

Tahmineh Azizi, Bacim Alali, Gabriel Kerr

Mathematical Modeling: With Applications in Physics, Biology, Chemistry, and Engineering, Edition-2, 26 June 2021, Page 1-117
https://doi.org/10.9734/bpi/mono/978-93-91312-16-9

A mathematical model can be defined as an abstract model which uses mathematical language to describe the behavior and evolution of a system. Mathematical models are used widely in the many different sciences and engineering disciplines (such as physics, biology, chemistry and engineering). Mathematical models may have many different forms, including continuous time and discrete time dynamical systems (using differential equations an difference equations respectively), statistical models, partial differential equations, or game theoretic models. Mathematical modeling has an important role in the discovering the problems which occur in our daily life. Mathematical and computational models has been frequently used to help interpret experimental data. Models also can help to describe our beliefs about how different phenomenon around the world functions. In mathematical modeling, we try to transfer those beliefs and pictures into the language of mathematics. This transformation is very beneficial. First, Mathematics is an exact and delicate language. Second, we can easily formulate ideas and also determine the basic assumptions. The governed rules in Mathematics help us to manipulate the problem. Strongly speaking, in Mathematical modeling, we are using the results which have been already proved by mathematicians over hundreds of years. Computers play an important role to perform numerical simulations and calculations. Although, many of the systems in the real world are too complicated to model but we can solve this problem by identifying the most important parts of the system and then we include them in the model, the rest will be excluded. Afterward, computer simulations can be applied to handle the model equations and desired manipulations.