1. A subsystem of a given system: a system which is a subset of the given system, and its rules describing relations between the subsets of this subset agree with the rules for the given larger system. Open and closed systems: * an open system is a system which can be fully described only if it is described as the subsystem of a larger system; * a closed system is a system which can be fully described in itself in self-contained form, without invoking any larger system containing it.

2. (continued) Dynamical system: a system depending on one or more real parameters. This requirement simply means that the system depends on a real parameter (the real line is fully ordered which means that the parameter can be interpreted as time). * If the definition domain of this real parameter is a discrete mesh of real numbers, the dynamical system is called discrete-time or discrete-event (or simply discrete); * If the definition domain is an interval (possibly the whole real axis or its positive part) the dynamical system is called continuous-time, continuous-event (or simply continual). (Note that dynamical systems can have more than one independent time scale.)

3. (Continued) Physical and conceptual systems: * physical systems consist of (objectively existing) matter (in the form of mass, energy or electromagnetic, gravitational or other field); * conceptual systems consist of (subjectively existing) concepts. Mathematical models are conceptual systems which describe approximately physical or other conceptual systems. It is possible to construct also physical realizations of many mathematical models, e. g., for the purposes of visualization. Simulation is also often considered only conceptually (independently, say, of the concrete computer platform), but the physical aspects (depending on concrete computer, concrete temperature in the moment of computation, queues and memory distribution, etc.) are also important in many cases, especially ones related to industrial applications. Another example of physical mathematical models and simulation are provided by non-digital analogue methods (appeared before the digital computer was invented). Unless explicitly specified otherwise, we shall consider, by default, only the conceptual aspects of mathematical modelling and numerical simulation.