This is the first book on the problems of mathematical modeling that combines a generalized approach to the problem of mathematical modeling processes and phenomena in the real world with developing modeling methods in relation to specific objects and processes. Some of the problems discussed here include stability and bifurcation of simplified models of supply and demand, and resultants of various approaches, such as standardization, unification and partial order, data packaging.As well as touching upon the general principles of modeling, the book studies the stability of mathematical models using the generalized 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 well-known specialists in the field of qualitative theory of equations and problems of modeling real-world phenomena, this book is primarily targeted at specialists in the field of engineering sciences, but is also suitable for graduate courses.