System Variability Over Time (in combination with internal heterogeneity, structuring, functioning, and development of the system)

A discussion of the dynamics of processes at the inputs and outputs of the system is a consideration of changes occurring outside the system, although directly on its borders with the environment. However, in many situations of interactions with the system, the subject needs to know also what is happening inside the system, “how the system works”. This is especially characteristic of those situations of control when the design of the control action relies on how exactly the interaction between parts of the system will occur as a result of impact. This third section of system dynamics is devoted to this topic.

The development of a management decision is aimed at finding such an impact on the system that will lead to the desired response, that is, to the implementation of the desired process at the output of the system. In this formulation of the question, it comes down to finding a “leverage” point of influence on the system and trying to predict what kind of impact on this keypoint will lead to the desired behavior of the system. This usually requires information about w'hat processes take place in the system, that is, information contained in static and dynamic models of the composition and structure of the controlled system.

For artificial, “hard” (and, in particular, technical) systems, such information is presented in the form of a complete structural scheme (combining models of composition and structure), the technical documentation that is created during the design and construction of the system. Whatever the problem may arise in such a system, in its structural scheme, we can find the part of the information that is needed to solve this problem.

With “soft” (especially biological, social, and environmental) systems, the situation is quite different: all information about the system is embodied only in the system itself, and often the part of the information that will be needed in this situation will have to be extracted from the system itself. If it is necessary to solve the problem, it is necessary to build the necessary models based on the results of direct study of this problem situation. Technical details of the entire process of practical problem-solving are described in Part II of the book; here we will focus only on the construction of models of the functioning of a complex system. These models allow us to move forward in identifying the causes of the problem, which is a very important step toward its solution.

Modeling begins w'ith building a model of the composition of the problem situation, making a list of all significant participants (stakeholders, see Section 5.3 in Part II) of the situation in question.

For illustration, we will provide such lists for imaginary situations (in real situations, much more details should be taken into account). The doctor, diagnosing the patient, considers not only the painful part of the body but also the condition of the patient’s other organs, and the factors of his habitat (lifestyle, living conditions). Businessmen in solving problems take into account not only the work of their enterprise but also the factors of the external environment (suppliers and consumers, competitors in the product market, the current legislation) and employee interests.

Subsequently, follow the efforts to build a model of the structure of the situation, the definition of essential relationships between the identified factors. The construction of the graph begins, whose vertices are the factors and the arcs are the relationships between them. Further (if necessary), this static model is “revived”: the direction of the influence of one factor on the other is determined (on the arcs are marked arrows, forming a directed graph); the nature of the influence is sometimes indicated only by “+” or near the arrow, depending on whether the first factor contributes to or hinders the second, or the nature of the influence is determined more specifically by the words (“determines”, “increases the probability”, “good/bad for”, etc.), such graphs are called labeled or signed; if you want to take into account the differences between the resources flowing in different arcs, they are displayed in different colors (colored graphs appear).

The difficulty of managing complex systems stems from the fact that the impact of some elements on other elements located in the remote part of the structural network is the result of changes in the flows flowing through several branches of the network, where each branch connecting them consists of a number of other intermediate elements. The constructed graph helps to understand the mechanism of such influence. For example, the effects of smoking on heart health can be shown (approximately, of course) as in Figure 8.1. It explains why the harm of smoking affects to varying degrees on the heart problems of different smokers: the balance of intermediate factors for each organism is individual.

However, the main difficulty in predicting the consequences of intervention in a complex system does not arise even because of the multiplicity and branching effects of parts on each other. Of great importance for how the processes in the system will evolve, is how the impact will be made on the most variable element itself. In most networks, there are not only “direct” chains of interactions but also “reverse” chains, according to which the impact returns to the initial point in a few steps and affects it, which triggers the next iteration of the impact on the behavior of the system.

The recurrent influence may be amplifying the original, and then such feedback is called positive, or reinforcing, but it can also counteract, weaken, and compensate for the initial change, and then it is called negative, or balancing, feedback. Positive feedback rapidly increases the deviation of the system from a stable state, bringing it up to disaster, while negative feedback tends to return the system to equilibrium. When there are several loops of negative and positive feedbacks in the structure of the system, the behavior of the system for us, committed to linear cause-and-effect

relationships, becomes unexpectedly complex and incomprehensible. In addition, the complexity of the situation, the difference between the response of the system to the control action from the “intuitively expected”, is greatly exacerbated by another factor in the dynamics of the system — the presence of delays and lags between incentives and responses in different parts of the system.

Due to the difference in the time intervals between exposure and reaction to it in different components of the system, the consequences in the behavior of the system from an immediate control action are stretched over time, so we have to talk about the short-term, medium-term, and long-term results of a single act of management. As a result, the system dynamics is such a situation that the forecasts of all the consequences of interference in the real system become unreliable and managers seriously talk about the surprising counterintuitiveness of the behavior of complex systems.

Factors Determining the Behavior of Systems

Consideration of the features of the dynamics of systems has led to the understanding that the type of behavior of the system (i.e., the specific nature of its response to external influences) is determined by a combination of many factors. The main ones are:

  • 1. the relationship between the subjective purpose of external influence, the objective purpose of the whole system, and the own objectives of the parts of the system;
  • 2. the topology of the structure of the system: that is, the configuration of the network of links between all parts of the system; the presence in the network of direct ties and feedback (positive and negative) and their specific combinations;
  • 3. the correlation between the speeds of resource flows through the channels between parts of the system, the channels capacities, and the amount of reserves of resources in the storage;
  • 4. the inertia of each part of the system (the value of the delay of its response to the input impact); the ratio between the times of the delay response to the stimulus in different parts, especially, in the controlled and controlling parts;
  • 5. the choice of “leverage point”, that is, a specific (local or global) aspect of the system, which it is decided to have an impact;
  • 6. the choice of a specific type of impact on the keypoint; for example, the direction and magnitude (and sometimes configuration) of the change in the controlled factor.

Each particular combination of these factors generates a characteristic response of the system to the impact. Each factor can be described by qualitative and quantitative indicators, and the slightest changes in any of the indicators of any factor may lead to significant differences in the behavior of the system. In this regard, modern systems dynamics is aimed at the elucidation of the structure of the set of behaviors of the system (i.e., on construction of various classifications of the processes occurring in systems).

Interesting (and useful for at least a partial understanding of what is happening in complex systems) results are obtained when considering the effect on the behavior of the system of combinations of not all factors at the same time, but only one or two of them. In some cases, processes can be described quantitatively; in more complex situations, it is possible to give only a qualitative, fuzzy description of the general trend of the process (nevertheless, such information is useful in working with the system).

We will briefly discuss the identified types of systems functioning.

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