Flows and Stocks of Resources

The processes of transportation of resources according to the structure of the system are easier to consider than others. The main parameters of the dynamics here are the speed of movement of resources in each channel (edge of the graph), linking a certain pair of system elements (nodes of the graph), and the volume (levels) of the resource reserve accumulated in each store. The limiting parameters are the capacity of the channel (the maximum speed of the resource flow in this channel) and the maximum volume of each store.

The processes are described by linear additive equations, familiar from school times on the problem of the pool with pipes, through which water flows in and out. Difficulties arise when it is necessary to comply with certain ratios between the levels of stocks in all the drives in the system, which poses the task of coordinating the speeds of all flows (e.g., the tasks of the economy associated with the ratio of supply and demand in the market, production and distribution of goods, the inflow and outflow of labor resources of the enterprise, etc.). However, this task is not among the complex ones if there are no feedbacks in the structure of the channel network.

Qualitative Models of Complex Systems Dynamics: Archetypes of Behavior

Any purposeful interaction of the subject with the system (whether it is the study of the system, the design of a new system or the management of an existing one) is carried out with the help of models of the system behavior, that is, the description of the processes occurring in the system in the process of interaction with it.

When controlling, it is important for us to know how the specific impact of xft) on the t'-th controlled input of the system will effect on the process у ft) on its j-th output. In other cases, it is important to understand why the system behaved this way and not otherwise. What quality of information we need, about which processes, and in which elements of the system, depends on the goals of the subject. The set of information about the behavior of systems, modeling (description) of various such processes and is the content of the system dynamics.

When working with complex (especially social) systems, it is not always possible to bring the modeling to the construction of an accurate, rigorous, mathematical model because of the practical impossibility of taking into account all the links between all elements of the system and the environment. However, often in practice we do not need all the information about the object; we need only the part that will allow us to achieve the realization of our specific goal. A clear analogy is the modeling of the same terrain with maps for different purposes. For some purposes, enough information provided on the globe; other purposes require a more detailed display of the various features of the area: there are maps of different scales and purposes — geographical, administrative, environmental, political, geological, demographic, topographic, military, secret, etc.

This situation is inherent in any kind of human activity (both practical and cognitive), including systemic dynamics. To date, efforts to develop theoretical models of system dynamics are intensively conducted in two directions: the development of quantitative and qualitative models of system behavior. The first direction, called synergy, focuses on the mathematical description of regularities (attractors) arising in the chaotic behavior of complex nonlinear systems. The second direction focused on overcoming the “counterintuitiveness” of complex systems by finding out what features of the system structure cause this or that character of the functional behavior of the system.

Very few systems (e.g., cells multiplying by division) appear immediately in a perfect state for themselves. For most systems, the lifecycle is a period of gradual changes in their composition and structure, and the corresponding changes in their functions (properties). Changes can be very diverse: quantitative and qualitative. They can occur at different rates and have monotonous or variable trends. Often there are processes that are nonlinear (nonadditive) result of the interaction of two or more characteristics; and almost always such processes are generated as a result of the feedback action, and the variety of forms of nonlinear curves is associated with a variety of combinations of a certain number of feedback loops and (or) delays in the branches of the network of links. Different combinations of feedback loops in the system structure give rise to different types of system behavior. Each configuration of loops in the structure of the system generates a special, inherent only to it, the type of behavior of the system as a whole.

The fundamental result of the rapid development of system dynamics in the 80s of the last century was the identification of characteristic (different quantitatively, but qualitatively the same occurring in different systems) types of behavior of systems. In the synergy, these are attractors; in the qualitative theory, these are archetypes. In the latter case, it was found that some certain types of behavior correspond to the presence in the structure of the system of certain configurations of feedback loops and certain relations between the delays in the reaction of parts to the incoming effects. Such qualitatively different classes of systems behavior are called archetypes; to date (2014), more than a dozen archetypes have been identified and explained (this work was started by J. Forrester, and continued by J. Kennedy, M. Goodman, P. Senge, D. Medows, etc.).

We note that, in practice, pure archetypes occur only when the structure of the system is indeed dominated by the configuration of relations that generate this type of behavior. The degree of influence of this configuration on the behavior of the system as a whole can be weakened and distorted as the influence of other components of the system structure increases and the corresponding degree of dominance of this configuration decreases. The basic components of any network structure are linear chains of connections between elements and feedback loops. A single feedback loop circuit may involve a different number of elements of the system, and the relationship between each pair of elements in this circuit may have a different character

(reinforcing — positive, or weakening — negative). What kind of feedback (negative or positive) forms in the end the entire circuit, consisting of several pairs of elements, depends on whether even or odd number of weakening links is in the whole chain: an odd number of them (1,3,5,...) formed a negative feedback, and even (0,2,4,...) positive feedback (Figure 8.2); in this form, the law of dialectics “Negation of negation” is manifested in this case.

In turn, the structure of the system may contain a different number of feedback loops in different combinations: the loops may be separate, may have common elements with other loops, may themselves be included as components in other loops (Figures 8.3 and 8.4), etc.

FIGURE 8.2 Combinations of different links in feedback.

FIGURE 8.3 Combination of one feedback loop with one common element.

FIGURE 8.4 Combinations of two feedback loops with two common elements.

Different combinations of feedback loops in the system structure give rise to different types of system behavior. Each configuration of loops in the structure of the system generates a special, inherent only to it, the type of behavior of the system as a whole. This is how the “archetypes” of system dynamics manifest themselves.

Let us begin our consideration of archetypes with the simplest case — the predominance of one feedback loop in the structure of the system.

The archetype of growth of the system. Any (one-dimensional) process can be represented as a graph of the time dependence of the parameter we are interested in over time. In the most intricate curve one can distinguish “elementary”, “simple” intervals of the same type and start explaining the whole process with an explanation of the origin of a particular interval.

Let us turn to the case of monotonic changes in certain characteristic of the system. For example, linear growth or decline of the graph is typical for a change in the stock of resource X(t) in the accumulator under a constant speed difference, ^vm ^{- v}oui between the inflow and outflow of resource: X(t) = (v_in - v_oul) • t (see Figure 8.5).

In the dynamics of growth of systems, there are often cases of faster than linear (i.e., directly proportional to the time) increase. The reason for this is the influence of positive feedback, leading to exponential growth (see Figure 8.6).

This (under certain conditions) occurs with the size of living population (including the population of the earth), the level of pollution of the human environment, the degree of drug dependence, epidemics, explosive chemical and nuclear reactions, etc. The account in the bank with the annual accrual of simple interest

FIGURE 8.5 Linear trends.

(without feedback, only the invested amount) grows linearly over the years, and with compound interest (with feedback, i.e., when calculating the principal amount together with the interest of previous years), the amount of the account grows exponentially. For example, with an annual 10% amount of 10,000 rubles in 56years will turn into 66,000 rubles with simple interest, and with compound interest, 1,280,000 rubles.

Archetype of regulation. Single negative feedback loop (without delays!) produces a monotonic approximation of the value of the parameter X to a given (target) level X₀: if the initial state exceeds the target, the feedback gradually reduces it to the target; if the initial state is below the target, it increases (see Figure 8.7).

Appearance of delays in the communication channels between the elements significantly increases the variety of types of behavior of the system, further generating nonmonotonic (including oscillatory) processes. For example, a delay in the negative feedback loop leads to fluctuations due to delays in the regulation of controlled parameters (see Figure 8.8).

Even in such a relatively simple structure as in Figure 8.8, the nature of the resulting process is highly dependent on the ratio of delays (inertia) of the controlling and controlled systems. (Examples include the fluctuations of the difference between supply and demand on the markets for many products, the sinusoidal character of the trajectory of the car on the road, fluctuations of the regulated parameter around the target value in automatic control systems, temporal variations in the abundance of animal populations of predators and prey, fluctuations in the value of the shares on the stock exchange, etc.)

FIGURE 8.7 Regulation without delay.

Let us now consider the archetypes associated with the two interacting loops of feedback.

Archetype of Drifting Goals (“Erosion of goals”). The difference between the existing and target states of the system can be reduced in two ways: by bringing reality closer to the goal, and by lowering the level of targeted claims. The last scenario of behavior is this archetype. It is characterized by the gradual lowering of targets leading to the degradation of the system.

Different (internal and external) reasons can force to decrease claims, to force to pay more attention not to that it would be desirable to happen (i.e., the purposes), but to that something did not occur (i.e., to decrease of the purpose). For example, people who reduce their demands are gradually becoming less successful; the country’s budget deficit leads to economic crises; reducing investment in the development of the company is actually a form of lowering product quality standards; the weakening of environmental requirements for acceptable levels of pollution reduces the quality of life in it. Structure of feedbacks that causes the archetype is shown in Figure 8.9.

Note that two negative feedback loops form one “eight-shaped” positive feedback loop (with an even number of weakening links in this chain of links), which leads to the approach of the crisis. Delays cause short-term measures to collapse in the long run. (Clear allegory: plopped in hot water, the frog will instantly jump out of it; but if the water is heated gradually, the frog suffers until it is boiled.).

The “Escalation” Archetype. If there are no delays in the structure of the two negative feedback loops, the crisis escalates as an avalanche (due to the eight-shaped positive feedback loop). Each of the opposing sides considers the actions of the other side as a threat to themselves, and further strengthens its aggressiveness in response to the increased aggressiveness of the opponent. For example, the escalation of the cold war into a hot war (as at the beginning of the Caribbean crisis), transition of the subjects’ dispute to the judicial phase (in particular, divorce proceedings), tough competition in business, rivalry for influence on the chief in bureaucratic structures, arms race, and uncompromising fight against terrorism.

The structure of the links leading to the escalation events is shown in Figure 8.10.

A cessation of the escalation is possible either in the transition from competition to cooperation as a result of finding a common goal covering the goals of both sides, or in the unilateral termination of the confrontation. Otherwise, the conflict enters an irreconcilable phase.

Archetype “Limits to Growth”. A separate class of changes is a quantitative increase in a certain characteristic of the system (internal—size, mass, number of elements; or external—force, stress, speed, beauty, superiority, power, etc.). This type of change is called growth (of this characteristic).

However, the growth may have a different character. It is found that the accelerating growth is associated with the action of a single positive feedback loop (see “Archetype of growth”). In reality, however, growth never lasts forever; this is due not only to limited resources for growth but also to the fact that other feedback loops and delays in them are involved in the process. This led to the identification of another type of behavior of the growing system — the archetype “Limits of growth.”

This archetype is characterized by the fact that the initially accelerated growth of the system begins to slow down and, despite the persistent continuation of successful in the past efforts, completely stops (stagnation occurs) or even goes into a recession stage (crisis, recession). Typical graphs of such a process and a block diagram of the archetype (of two opposite-valued feedback loops) are shown in Figure 8.11. Constraints to growth may be of internal and/or external, resource or legal, material or cultural origin. Symptoms of the archetype: At first, “We are growing remarkably;

FIGURE 8.10 Archetype “Escalation”.

we have nothing to worry about.” Then, “The problem is, but we will solve it, acting as before.” Finally, “Despite all efforts, we are growing more slowly.”

Examples of this archetype are observed in the form of a corresponding lifecycle graph (see Figure 3.18) in all types of systems. So is the curve of sales of a new product in economic systems behaves; so is the vital activity of any biological individual changes; such character is the history of all empires; such forecasts of the state of the world economy are given by the “Roman Club” [6]; and “Everything has its end, and its beginning”, as the poet said.

The causes of this archetype of behavior can be both outside and within the system and be of a diverse nature. The possibility of postponing the crisis or reaching a stable state is to identify the causes of the slowdown and take measures to counter them.

For example, the annual planned growth of production requires from the company not only a corresponding increase in material resources but also an increase in the number of employees with the necessary skills, and the time of training of new such personnel is much longer than the time of the planned increase in production volumes. If training is not started long before it is needed, a decline in production is inevitable.

Another example is given by the forecasts of the Club of Rome [6]: on the computer model of the dynamics of the world economy, 13 scenarios were calculated, differing in what combination of growth inhibition factors are regulated (extraction of natural resources, pollution of the environment, land productivity, resource-saving technologies, population numbers, volume of industrial production, food production, fresh water resource size, etc.). Twelve of them differ only in the timing of the final global crisis, and only one promises to reach a stable level, with the change of mental models (the paradigm of the meaning of life), the rejection of consumer attitudes to technological progress.

The archetype of the Ineffective amendments” (Fixes that Fail). This type of situation often occurs when trying to correct the deterioration of the situation in some way, giving a positive effect only briefly, after which the deterioration resumes with renewed vigor. This is often unexpected; but sometimes a person is aware of the negative consequences of the corrective action taken, but either the desire to immediately get relief exceeds the fear of long-term consequences (as in the removal of a heart attack), or he simply does not see another way out (as in the desire to increase sales by increasing investment in marketing due to their reduction in the development of production).

Knowledge of the mechanism of this archetype can help to get out of it, getting into it unexpectedly, or even consciously refrain from entering it. The nature of the dynamics of this process and its causing structure of two different types of feedback loops are shown in Figure 8.12.

The reason for its occurrence is that the action taken has, along with the desired (quick and short-term) consequences (in the negative loop), also unaccountable negative long-term consequences (this is shown in the diagram by the presence of a delay in the positive feedback cycle). In other cases, the cause of falling into this archetype is the initially erroneous acceptance of the symptom of the problem for the problem itself, the means to achieve the goal for the goal itself. (For example, “the problem is that we don’t have (or lack) something” or “...to implement modernization”). Overcoming of this archetype (as well as all others) can be carried out with the help of technologies of applied system analysis (see Part II).

FIGURE 8.12 Archetype “Ineffective repairs”.

FIGURE 8.13 “Success to successful”.

The archetype “Success to the Successful”. It is stated that out of two equal systems A and В in the rest, the winner is the one whose initial resource is greater: the first success A is rewarded with an additional resource, which leads to a further increase in its success. The block diagram of this archetype is shown in Figure 8.13.

Examples: Encouraging successful athletes: increased attention to training promising professional athletes; creation of elite educational institutions for gifted children. The only possible order generally accepted only because at first it was followed by the majority: the direction of movement of clock hands, different directions of writing for Europeans (from left to right), Arabs (from right to left), and Japanese (from top to down). The principle of bank finance “Money to money”.

However, this archetype has negative aspects. The first is the final emergence of a monopoly position in this area. In some areas (such as sports) this is a desirable goal, in others, it is undesirable (e.g., in the economy it destroys competition, which is why the state takes antitrust legal restrictions). The second was called the “Trap of self-sufficiency” (Competence Trap). Sometimes a high level of previously successful activity is maintained (despite the drop in external demand for it!) only because we are able to do this activity better than others. A good example of this is the history of IBM (Figure 8.14).

Having become a monopolist in the production of large computers (mainframes, MF), the firm, confident in their superiority over the emerging PC, poorly invested

FIGURE 8.14 “Trap of competence” for IBM producing of MF.

in PC, which led to the loss of the market. The emergence of the PC did not change IBM’s opinion about the reasons for its success (“users need productive MF”), and the company did not react to the fact that the reason for the success of the product with the consumer was the best ratio of its price and quality. As a result, IBM lost the PC market. In a similar trap of their own competence is a qualified teacher of the university, insisting on increasing the hours of its well-established course, and does not want to develop a new course for themselves. The reason for the “Competence Trap” is the discrepancy between internal and external criteria of success.

Let us now consider some behavioral archetypes that appear in cases when the structure of the system is dominated by more than two loops of feedback.

Archetype “Shifting the Burden”. In practice, complex problems are often addressed by addressing the symptom of the problem rather than the cause. A side effect of this choice of the leverage point is that the relief of the symptom creates the illusion of a solution to the problem and distracts from the search for its fundamental solution.

The structure of connections that generates this archetype is shown in Figure 8.15.

Examples are attempts to solve the problem of alcoholism by banning the production and sale of alcohol, the problem of road crashes by increasing fines for traffic violations, the problem of crime by increasing punishment, the problem of stress by taking a dose of alcohol or drug, the problem of paying debt through a new loan, the problem of increasing profits by expanding the traditional segment of the market instead of diversifying production, etc.

One version of this archetype is so widespread and often so harmful that it is worth a separate mention. This is a case of trying to solve the problem only through external efforts, without mobilizing internal capabilities, that is, “Shifting the burden to a third party”. There are times when external assistance mitigates the problem to such an extent that the problem carriers themselves lose interest in solving the problem by their own efforts. For example, in some countries, the multichild allowance allows parents to avoid productive work at all; one-time care for genetic patients distracts attention from taking measures to prevent their occurrence

The main principle of external aid management is “Teach them to fish instead of giving them fish.” If external assistance is needed, it must be either one-time (and everyone knows this in advance) or aimed at developing the capacity, resources, and infrastructure of the system to succeed on its own in the future, without external assistance.

Archetype “Growth under Underinvestment”. This archetype is associated with the situation when the growth of the company reaches a limit that can be surpassed

FIGURE 8.15 Archetype “Shift of a burden”.

only with additional investment. However, the company can continue to increase production, by reducing the requirements for product quality. This creates the illusion of unnecessary additional investments in production, justifying its further underfunding. But the decline in the quality of goods or services inevitably leads to the displacement of the company from the market. This behavior of the firm follows from the interaction of three feedback loops, combining the archetypes “Limits of growth” and “Erosion of goals” (Figure 8.16).

A symptom of this archetype is that the firm does not attach importance to reducing the quality of its product, but instead blames competitors or its sales department for insufficient sales efforts.

The way to avoid falling into this archetype is to preempt events: if the conjuncture promises real opportunities for growth in demand in the future, the company’s strategy should include preparation for this in advance, to begin training the necessary personnel, to create the necessary reserves of resources in a timely manner, to monitor compliance with quality standards, etc.

Archetype “Tragedy of the Commons”. This archetype characterizes the situation when all members of the group use a limited, publicly available resource, each satisfying only its own interest. As the resource decreases, everyone tries to increase their consumption, which only accelerates the depletion until the complete exhaustion of the resource.

Examples of this are not only the situation with the consumption of nonrenewable resources but also renewable resources when the rate of consumption exceeds the rate of growth of the resource: traffic jams in cities (resource consumed is traffic capacity of roads); the disappearance of many species of game animals, fish, and plants; pollution of soil, water, and atmosphere by industrial and household human waste; a shortage of qualified personnel in the economy; etc., The structure of the

FIGURE 8.16 “Growth under shortage of investments”.

FIGURE 8.17 “Tragedy of the commons”.

network of feedback loops and delays that generate the archetype is given (for the case of two consumers of the resource) in Figure 8.17.

To postpone the tragedy (for a nonrenewable resource) or to prevent it (for a renewable one), it is possible only by developing and implementing a strategy of rational regulation of the use of the resource, which harmonizes short-term individual and long-term collective interests.

About other archetypes. We describe the behavior of this system in this environment as a set of processes occurring at the system outputs (i.e., as a set of its functions, see Sections 2.1 and 2.2, Part I). Each function is the result of the interaction of all parts of the system (see Section 2.3). However, in what happens at this output, different parts of the system play different roles, which differ not only qualitatively but also quantitatively: the influence of the actions of some parts is more significant than the others (e.g., the absence of one finger did not prevent Yeltsin from playing volleyball perfectly, but excluded the opportunity to play the piano). As a result.

in the formation of a specific function, the determining role is played not by the entire network of elements of the system, forming its structural scheme, but only by certain part of it. The structure of this part determines the nature of the process at this output: what and how many feedback loops, and in what combination they participate in this substructure, and determines what is called the archetype.

Thus, a process can be considered as an archetype when it interests us more than others in the behavior of the system. To understand why it happens this way, it is enough to identify the features of the substructure that determines this process. If this process is undesirable, you should rebuild this substructure appropriately, creating a new archetype.

A good example of this situation is considered in the case of Marilyn Paul “the Transition from mutual accusations to mutual responsibility” [7]: “When something goes wrong, most often the first question we ask is ‘Who is to blame’?. In many organizations, the search for the perpetrators is similar to the conditional reflex. Even those who wish to learn from mistakes are tempted to find guilty ones.

However, there are problems with this: before the threat of accusations, people close, the investigation comes to a standstill, the desire to understand the essence of what is happening sharply narrows. In the atmosphere of the impending accusations, there is a natural desire to hide their mistakes, to hide the true motives, and to blame someone else.”

M. Paul [7] established two systems of feedbacks together causing this behavior. First, positive feedback loops increase the difficulty of solving the problem (Figure 8.18). Accusations cause fear, which increases secrecy and reduces the flow of information. Lack of information hinders problem-solving by increasing the number of errors (internal loop). Fear also suppresses the willingness to take risks in the future and the desire to innovate (second cycle).

Second, the “burden-shifting” archetype is involved in the situation, making it difficult to realize that the fault is common, and reducing the ability to make

FIGURE 8.18 Inclination to blaming.

FIGURE 8.19 Increasing of blaming.

common efforts to solve the problem (Figure 8.19). The announcement that someone is to blame alone only briefly creates in majority the illusion of relief of guilt (the upper loop of positive connection). This reduces the desire to share information and communicate effectively (external positive feedback), and undermines the ability to develop mutual responsibility (lower negative connection loop).

Discussing the shift away from mutual accusations to mutual responsibility, M. Paul characterizes the differences between them as follows:

At the end of the consideration of the phenomenon of archetypes of systems behavior, once again we emphasize that it is based on finding the “main reason” for this type of system behavior: “this is the result of the action of such a combination of feedbacks and delays”.

However, in reality, the result is influenced not only by this combination but to some extent the other components of the system. The degree of clarity of the archetype depends on the degree of predominance of the influence of its characteristic substructure over the influence of other structures. This explains the fact that the severity of the conflict is different, and the implementation of recommendations in different organizations to overcome the undesirable archetype leads to success to varying degrees.