Among the system characteristics is a set of properties that a system characteristic. They arise on the one hand from the properties of the elements of the system and on the other hand from the system structure , i.e. their relationships with one another.
It is characterized by the type and number of elements as well as the type, strength, number and density of interrelationships on the micro level.
The complexity or complexity is determined by the number of elements and the number and type of relationships. A distinction is made between structural complexity (quotient of the number of relations and elements; degree of complexity = K = no / ne) and temporal complexity. This means the number of possible states that the system can assume in a period of time.
Description of the extremes:
|simple systems||complex systems|
|Number of elements||low||big|
|Similarity of the elements||the same in all characteristics||different in all characteristics|
|Amount of relationships||low||big|
|Relationship density ( degree of networking )||low||big|
All degrees of expression are possible between simple and complex systems.
The complexity of a system depends on the definition of the system boundaries, the number of elements considered relevant and the interdependencies considered relevant . Many complex systems have a hierarchy-like structure: the closer (temporally and / or spatially) you get, the more details become visible. The same structures can occur again and again regardless of the scale. In this case there is no hierarchy, but rather self-similarity . In biology, self-similarity is less to be found in structures (but see cauliflower ) than in basic principles, e.g. B. the rules of evolution (overproduction - variation - selection ) apply on all structural and time levels.
It is characterized by the behavior of the system over time. Without external influences, static systems show no changes either on the macro level or on the micro level (example: stationary pendulum ). Dynamic systems are subject to constant changes on the micro level, but can at least temporarily assume a steady state on the macro level (examples: chemical equilibrium reaction, forest ecosystem ). Whether a system is viewed as static or dynamic depends on the time scale and the duration of the observation of the system. This becomes clear with systems in equilibrium, which, however, fluctuate around their equilibrium position: If the observation period is too short, it cannot be determined whether the fluctuations are a mean value or whether there is an increasing or decreasing trend (example: climate fluctuations since the beginning of the direct measurements). If a very large scale is chosen, the fluctuations cannot be determined at all; the system seems to be static.
Systems and elements are linked by relationships. These relationships can be energy, material and information flows.
Possibilities at the macro level:
- Isolated systems have neither a substance nor an energy exchange with the environment.
- Closed thermodynamic systems can exchange energy with the environment, but not substances.
- Open systems exchange both materials and energy with the environment.
Depending on the defined system boundaries, a system can be viewed as isolated, closed or open, as the distinction between system and environment depends on this.
Isolated and closed systems practically do not occur in reality, but their modeling is necessary when investigating very complex systems.
Determination is the degree of “predeterminedness” of the system: A system changes from a state Z1 to a state Z2: Z1 → Z2. In deterministic systems this transition is determined (imperative), in stochastic systems it is probable .
In principle, deterministic systems allow their behavior to be derived from a previous state, stochastic systems do not. Classical deterministic systems allow an unambiguous determination of their state at any point in time in the past and future with sufficient accuracy (example: planetary motion ). It is sufficient here in relation to humanly manageable or relevant time periods and orders of magnitude. The development of chaotic systems cannot always be clearly determined, since all parameters must be known with theoretically infinitely great accuracy, they are sensitive to the initial conditions. With suitable (mathematical) models, relevant statements about the past and future of deterministic and stochastic systems can be made. From the complexity of a system, no statement can be made about the predictability : There are simple deterministic systems that are chaotic (e.g. double pendulum ) and complex deterministic systems ( chloroplasts during photosynthesis ).
Considerations of the reaction of a system on the macro level in the steady state to external disturbances
|options||stable||metastable||unstable, unstable||borderline stable , indifferent|
|reaction||returns to the original state||returns to the original state or changes to a new stable state||does not return to the original (unstable) state||every disturbance leads to a new (stable) state|
|Example chemical system||Systems with minimum enthalpy and maximum entropy||A hydrogen-oxygen mixture is stable until activated, then it reacts to form water||activated transition state||Diluting sulfuric acid|
|Example bar pendulum||The focus is below the pivot point||The focus is above the pivot point||The center of gravity and pivot points coincide|
Consider the elements at the micro level
In stable systems, the structure of the system does not change. The number, type and interaction of the elements remain constant. In unstable systems, slight changes in the system conditions are sufficient to bring about a change in the structure. These can be generated both from the outside and through internal dynamics.
With increasing complexity, the interchangeability of the elements and thus the structural stability is lost. If, in highly complex systems, an element is exchanged for another that no longer has the same properties, the overall behavior of the system can change (example: organ transplantation ).
Which stability of a system is determined depends on the specified time scale and the observation period as well as on the definition of the disturbance: Some stable systems change into unstable states if the disturbance is sufficiently strong (example: activation of chemical reactions ). All systems can be destroyed in the event of severe interference.
Dependency of the assignment of system boundaries
The assignment to one of the stability categories also depends on the definition of the system boundaries:
Example ball / bowl system
In the event of a fault, i. H. If the ball hits the ball, it rolls back to its starting position. Too strong a push will push the ball out of the bowl and the ball will fall to the ground. The original system is thus destroyed. If, however, the system ball / bowl / floor is considered, the ball in the bowl is only in a metastable state, since it assumes a more stable state on the floor.
If the ball lies on an inverted bowl (unstable system), every disturbance also leads to destruction. But if the inverted bowl / ball / bottom system is considered, every disturbance leads to a new state.
Example bar pendulum
Here, the system can adopt three different states depending on the position relationship between the center of gravity and the pivot point , which behave differently in relation to disturbances: Eccentric arrangement: There is exactly one stable state, all other states are unstable. For another pendulum system with centric support (pivot point and center of gravity coincide) there are infinitely many possibilities for aligning the beam, but all of them are unstable.
Time variance describes the dependence of the system behavior on the point in time at which it is viewed. A time-variant system behaves differently at different times. In technical systems, the reason for this is mostly due to time-dependent parameter values; in biological systems, for example, different environmental conditions. Time-invariant systems, on the other hand, behave the same at all times. A mechanical watch, for example, is time-invariant if wear is neglected. A pendulum in which the length of the suspension changes over time is time-variant.
|DIN EN 61069-1|
|title||Control technology for industrial processes - determination of system properties for the purpose of assessing the suitability of a system|
The European standard EN 61069-1 suggests the system properties shown in the table as a basis for self-assessment of a system in control technology . The standard is published in Germany as DIN standard DIN EN 61069-1.
|Functionality||Operating behavior||reliability||Usability||safety||Not task related|
- discrete (time or state discrete) - continuously
- linear - non-linear
- purpose-oriented or goal-oriented
- adaptive (adaptive)
- autonomous (independent of external control)
- autopoietic (self-reproducing)
- regulating, self-regulating
- trivial - nontrivial
- distributed / concentrated parametric