By the nature of the displayed properties of the designed object mathematical models are divided into functional and structural. 
On how to obtain the functional model is divided into theoretical and formal * Theoretical models are obtained by study of physical laws, the structure of the equations and parameters of the models have a definite physical interpretation. 
Formal models are obtained by manifestation of the properties of the object in the external environment, ie, when considering the object as cybernetic "black box". Depending on the linearity or nonlinearity of the equations of the model is divided into linear and nonlinear.

Therefore, most mathematical models formulated in the form of equations relating the physical quantities that characterize the state of the object and do not belong to the above output, internal or external parameters. These values are called phase variables.Vector of state variables defines a point in space called the phase * phase variables that directly characterize the energy reserves in the elements of the system-theme, called state variables. Output parameters for such an approach makes sense functional dependence of the phase variables of time.