Meta-systems have several definitions. In general, they link the concepts "system" and "meta-". A "meta-system" is a system about other systems, such as describing, generalizing, modelling, or analyzing the other system(s).
It means, if a system S is described by the set of attributes A and these attributes are considered as abstract objects (with their own properties/attributes), then their interrelations may form a meta-system of S.
For example, let a system Sx be described by measured objects (temperature, pressure, volume, etc.), then the general relation between abstract objects: temperature, pressure, volume, i.e. P*V/T =constant (the ideal gas equation) defines the meta-system known as "meta Sx". Also, the description of the structure of a given system is its meta-system.
According to Turchin and Joslyn (1997), this "natural" systemic definition is not sufficient for their Theory of Meta-system Transition,[1] it also is not equivalent to the definition of system of systems in Autopoietic Systems Theory,[2] and it differs from the definition proposed by K.D. Palmer.[3]
In the above context, systems of systems are not meta-systems, and a few local domain-dependent definitions of meta-system are used.
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In economics, meta-systems are like what Bataille calls general economies as opposed to the restricted economies of systems.
A book about the difference between general and restricted economies is Complementarity by Arkady Plotnitsky. In this case "meta" is defined as what is beyond: the meta-system is what lies beyond the system.
In mathematics, biology and psychology, many variables have occurred within structures and systems that determined the results, discoveries, rates and value(s) of sets, systems, and developments within systems, structures, systems within structures and sets of structures.
A mathematical-modelling rule system for a domain D is an example of a meta-system in mathematics and science, for similar and consistency of concrete or frequency found in models within a domain. These are all modes or models; where commonalities are more consistent with consecutive scores or values within a ranged order and are good indicators for gauging probabilities traits (psychology) or properties (biology).
Meta-systems in cultural studies and sociology refer to contexts, milieux, situations, ecosystems, environments and the biological process with the use of commonalities in behavioral traits and human developments found surrounding a social or scientific system which the system must interact with in order to remain viable. Meta-systems have different structures and also are complementary to other structures of such systems. Without this complementarity in the values, bondings, or tact the systems could not remain productive, viable or operational.
The term "meta-system" (or "metasystem") in cybernetics is synonymous with management system or control system. Stafford Beer, who founded management cybernetics with his Viable System Model, speaks of metasystems that apply metalanguages which are able to find means of making decisions when necessary improvements cannot be made. In computer science this is known as the halting problem. Here metalanguage works in a larger context than the language it describes and has more variety.