"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype. The prototype may be a physical, biological, social, psychological or conceptual entity, perhaps even another mathematical model." (Rutherford Aris, "Mathematical Modelling", 1978)
"The identification and selection of important descriptor variables to be used within an equation or process that can generate useful predictions." (Glenn J Myatt, "Making Sense of Data: A Practical Guide to Exploratory Data Analysis and Data Mining", 2006)
"Mathematical model is an abstract model that describes a problem, environment, or system using a mathematical language." (Giusseppi Forgionne & Stephen Russell, "Unambiguous Goal Seeking Through Mathematical Modeling", 2008)
"A set of equations, usually ordinary differential equations, the solution of which gives the time course behaviour of a dynamical system." (Peter Wellstead et al, "Systems and Control Theory for Medical Systems Biology", 2009)
"An abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science). It can be defined as the representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form." (Roberta Alfieri & Luciano Milanesi, "Multi-Level Data Integration and Data Mining in Systems Biology", Handbook of Research on Systems Biology Applications in Medicine, 2009)
"Mathematical description of a physical system. In the framework of this work mathematical models pursue the descriptions of mechanisms underlying stuttering, putting emphasis in the dynamics of neuronal regions involved in the disorder." (Manuel Prado-Velasco & Carlos Fernández-Peruchena "An Advanced Concept of Altered Auditory Feedback as a Prosthesis-Therapy for Stuttering Founded on a Non-Speech Etiologic Paradigm", 2011)
"Simplified description of a real world system in mathematical terms, e. g., by means of differential equations or other suitable mathematical structures." (Benedetto Piccoli, Andrea Tosin, "Vehicular Traffic: A Review of Continuum Mathematical Models" [Mathematics of Complexity and Dynamical Systems, 2012])
"Stated loosely, models are simplified, idealized and approximate representations of the structure, mechanism and behavior of real-world systems. From the standpoint of set-theoretic model theory, a mathematical model of a target system is specified by a nonempty set - called the model’s domain, endowed with some operations and relations, delineated by suitable axioms and intended empirical interpretation." (Zoltan Domotor, "Mathematical Models in Philosophy of Science" [Mathematics of Complexity and Dynamical Systems, 2012])
"The standard view among most theoretical physicists, engineers and economists is that mathematical models are syntactic (linguistic) items, identified with particular systems of equations or relational statements. From this perspective, the process of solving a designated system of (algebraic, difference, differential, stochastic, etc.) equations of the target system, and interpreting the particular solutions directly in the context of predictions and explanations are primary, while the mathematical structures of associated state and orbit spaces, and quantity algebras – although conceptually important, are secondary." (Zoltan Domotor, "Mathematical Models in Philosophy of Science" [Mathematics of Complexity and Dynamical Systems, 2012])
"They are a set of mathematical equations that explain the behaviour of the system under various operating conditions, and determine the dominant factors that govern the rules of the process. Mathematical modeling is also associated with data collection, data interpretation, parameter estimation, optimization, and provide tools for identifying possible approaches to control and for assessing the potential impact of different intervention measures." (Eldon R Rene et al, "ANNs for Identifying Shock Loads in Continuously Operated Biofilters", 2012)
"An abstract representation of the real-world system using mathematical concepts." (R Sridharan & Vinay V Panicker, "Ant Colony Algorithm for Two Stage Supply Chain", 2014)
"Is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour." (M T Benmessaoud et al, "Modeling and Simulation of a Stand-Alone Hydrogen Photovoltaic Fuel Cell Hybrid System", 2014)
"A mathematical model is a model built using the language and tools of mathematics. A mathematical model is often constructed with the aim to provide predictions on the future ‘state’ of a phenomenon or a system." (Crescenzio Gallo, "Artificial Neural Networks Tutorial", 2015)
"A mathematical model consists of an equation or a set of equations belonging to a certain class of mathematical models to describe the dynamic behavior of the corresponding system. The parameters involved in this mathematical model are related to a certain mathematical structure. This mathematical model is characterized by its class, its structure and its parameters." (Houda Salhi & Samira Kamoun, "State and Parametric Estimation of Nonlinear Systems Described by Wiener Sate-Space Mathematical Models", 2015)
"Description of a system using mathematical concepts and language." (Tomaž Kramberger, "A Contribution to Better Organized Winter Road Maintenance by Integrating the Model in a Geographic Information System", 2015)
"A description of a system using mathematical concepts and language." (Corrado Falcolini, "Algorithms for Geometrical Models in Borromini's San Carlino alle Quattro Fontane", 2016)
"A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)
"Mathematical representation of a system to describe the behavior of certain variables for an indeterminate time." (Sergio S Juárez-Gutiérrez et al, "Temperature Modeling of a Greenhouse Environment", 2016)
"A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g., computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology, and political science); physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behavior." (Addepalli V N Krishna & M Balamurugan, "Security Mechanisms in Cloud Computing-Based Big Data", 2019)
"A description of a system using mathematical symbols." (José I Gomar-Madriz et al, "An Analysis of the Traveling Speed in the Traveling Hoist Scheduling Problem for Electroplating Processes", 2020)
"An abstract mathematical representation of a process, device, or concept; it uses a number of variables to represent inputs, outputs and internal states, and sets of equations and inequalities to describe their interaction." (Alisher F Narynbaev, "Selection of an Information Source and Methodology for Calculating Solar Resources of the Kyrgyz Republic", 2020)
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