The concepts below have been synthesized from a number of sources, which are themselves summaries of concepts from other authors. Ackoff (1971) proposed a system of system concepts as part of general system theory (GST); Skyttner (2001) describes the main GST concepts from a number of systems science authors; Flood and Carlson (1993) give a description of concepts as an overview of systems thinking; Hitchins (2007) relates the concepts to systems engineering practice; and Lawson (2010) describes a system of system concepts where systems are categorized according to fundamental concepts, types, topologies, focus, complexity, and roles.
Wholeness and Interaction
A system is defined by a set of elements which exhibit sufficient cohesion (glossary), or "togetherness", to form a bounded whole (Hitchins 2007, Boardman and Sauser 2008).
According to Hitchins, interaction between elements is the "key" system concept (Hitchins 2009, p. 60). The focus on interactions and holism is a push-back against the perceived reductionist focus on parts and provides recognition that in complex systems, the interactions among parts is at least as important as the parts themselves.
An open system is defined by the interactions between system elements within a system boundary and by the interaction between system elements and other systems within an environment (glossary). The remaining concepts below apply to open systems.
Regularity
Regularity (glossary) is a uniformity or similarity that exists in multiple entities or at multiple times (Bertalanffy 1968). Regularities make science possible and engineering efficient and effective. Without regularities, we would be forced to consider every natural and artificial system problem and solution as unique. We would have no scientific laws, no categories or taxonomies, and each engineering effort would start from a clean slate.
Similarities and differences exist in any set or population. Every system problem or solution can be regarded as unique, but no problem/solution is in fact entirely unique. The nomothetic approach assumes regularities among entities and investigates what the regularities are. The idiographic approach assumes each entity is unique and investigates the unique qualities of entities, (Bertalanffy 1975). A very large amount of regularity exists in both natural systems and engineered systems. Patterns of systems thinking capture and exploit that regularity.
State and Behavior
Any quality or property of a system element is called an attribute. The state of a system is a set of system attributes at a given time. A system event describes any change to the environment of a system, and hence its state:
• Static - A single state exists with no events.
• Dynamic - Multiple possible stable states exist.
• Homeostatic - System is static but its elements are dynamic. The system maintains its state by internal adjustments.
A stable state is one in which a system will remain until another event occurs.
State can be monitored using state variables, values of attributes which indicate the system state. The set of possible values of state variables over time is called the "'state space'". State variables are generally continuous, but can be modeled using a finite state model (or, "state machine").
Ackoff (1971) considers "change" to be how a system is affected by events, and system behavior as the effect a system has upon its environment. A system can
• react to a request by turning on a light,
• respond to darkness by deciding to turn on the light
• act to turn on the lights at a fixed time, randomly or with discernible reasoning.
A stable system is one which has one or more stable states within an environment for a range of possible events:
• Deterministic systems have a one-to-one mapping of state variables to state space, allowing future states to be predicted from past states.
• Non-Deterministic systems have a many-to-many mapping of state variables; future state cannot be reliably predicted.
The relationship between determinism and system complexity, including the idea of chaotic systems, is further discussed in the Complexity article.
Function
Ackoff defines function as outcomes which contribute to goals or objectives. To have a function, a system must be able to provide the outcome in two or more different ways. (This is called Equifinality). This view of function and behavior is common in systems science. In this paradigm, all system elements have behavior of some kind; however, to be capable of functioning in certain ways requires a certain richness of behaviors.
The behavior of the resulting system is then assessed as a combination of function and effectiveness. In this case behavior is seen as an external property of the system as a whole and is often described as analogous to human or organic behavior (Hitchins 2009).
Hierarchy, Emergence and Complexity
System behavior is related to combinations of element behaviors. Most systems exhibit increasing variety; i.e., they have behavior resulting from the combination of element behaviors. The term "synergy", or weak emergence, is used to describe the idea that the whole is greater than the sum of the parts. This is generally true; however, it is also possible to get reducing variety, in which the whole function is less than the sum of the parts, (Hitchins 2007).
Complexity frequently takes the form of hierarchies (glossary). Hierarchic systems have some common properties independent of their specific content, and they will evolve far more quickly than non-hierarchic systems of comparable size (Simon 1996). A natural system hierarchy is a consequence of wholeness, with strongly cohesive elements grouping together forming structures which reduce complexity and increase robustness (Simons 1962).
Encapsulation (glossary) is the enclosing of one thing within another. It may also be described as the degree to which it is enclosed. System encapsulation encloses system elements and their interactions from the external environment, and usually involves a system boundary that hides the internal from the external; for example, the internal organs of the human body can be optimized to work effectively within tighly defined conditions because they are protected from extremes of environmental change.
Socio-technical systems form what are known as control hierarchies, with systems at a higher level having some ownership of control over those at lower levels. Hitchins (2009) describes how systems form "preferred patterns" which can be used to the enhanced stability of interacting systems hierarchies.
Looking across a hierarchy of systems generally reveals increasing complexity at the higher level, relating to both the structure of the system and how it is used. The term emergence describes behaviors emerging across a complex system hierarchy.
Effectiveness, Adaptation and Learning
Systems effectiveness is a measure of the system's ability to perform the functions necessary to achieve goals or objectives. Ackoff (1971) defines this as the product of the number of combinations of behavior to reach a function and the efficiency of each combination.
Hitchins (2007) describes effectiveness as a combination of performance (how well a function is done in ideal conditions), availability (how often the function is there when needed) and survivability (how likely is it that the system will be able to use the function fully).
System elements and their environment change in a positive, neutral or negative way in individual situations. An adaptive (glossary) system is one that is able to change itself or its environment if its effectiveness is insufficient to achieve its current or future objectives. Ackoff (1971) defines four types of adaptation, changing the environment or the system in response to internal or external factors. A system may also learn, improving its effectiveness over time, without any change in state or goal.