Mathematical Modelling

This is the first book on the problems of mathematical modelling that combines a generalised approach to the problem of mathematical modelling processes and phenomena in the real world with developing modelling methods in relation to specific objects and processes. Some of the problems discussed here include the stability and bifurcation of simplified models of supply and demand, and resultants of various approaches, such as standardisation, unification, partial ordering and data packaging.

As well as touching upon the general principles of modelling, the book studies the stability of mathematical models using the generalised direct Lyapunov method based on matrix-valued auxiliary functions. It has significant potential for application in the design of new moving objects (nano-robots, manipulators, drones, etc.) and processes related to artificial intelligence (multidimensional interaction of related data arrays) that can be described by differential equations of different types.

Written by two respected specialists in the field of the qualitative theory of equations and problems of modelling real-world phenomena, this book is primarily targeted at specialists in the field of engineering sciences, but is also suitable for graduate courses.

Contents:

• Model and Modelling, General Remarks
• Sets of Numbers and Modelling
• Orders, Rankings
• Average Rank Methods
• Modelling Elements, First Patterns
• Econometric and Economic Models
• Coronavirus and Other Models
• Facts about Population Growth, Mathematical Models
• Modelling Errors
• Stability Analysis of Mathematical Models

Readership: The primary target audience for this book are specialists in engineering and the natural sciences who are directly involved in modelling real-world objects and phenomena. The book is also suitable for senior undergraduate and graduate courses specialising in mechanics and applied mathematics, systems analysis and cybernetics.