3. System Dynamics. 3.1 System Dynamics as the Simulation Technique for Social Systems

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1 3. System Dynamics With the recent social and economic development, many social issues such as environmental issues, food problems, depopulation and aging, and garbage problems have become obvious. Environmental issues and food problems are on a global scale, while other issues are considered as regional. It is very difficult to design investigations to clarify causes and the problem solutions because these social issues have been derived from various complex human activities. To resolve these social issues, it is necessary to clarify the relationship among various events in the field as a whole. In addition, we need to clarify the mechanisms that induce these issues. For this purpose, an approach that investigates the cause of social issues by considering the society as a model and connecting every causal relationship among events is effective. We can thereby understand the society through the behavior of the social model, and consequently predict future situations. System Dynamics is one of the computer simulation techniques that are very useful for understanding the society based on logical thinking. In this chapter, the concepts of system dynamics and its application fields are introduced. 3.1 System Dynamics as the Simulation Technique for Social Systems System dynamics (SD) is one of the numerical simulation techniques that was developed in the late 1950s by J. W. Forrester of the Massachusetts Institute of Technology. He applied the methodology for system analysis used in engineering to dynamically analyze systems in the field of business administration and social science. He wrote Industrial Dynamics for the analysis of corporate activity, Urban Dynamics for the analysis of urban planning, and finally, he had reached a point at which SD had matured into a simulation tool for large-scale society system. In The Limits to Growth, which was published by the Club of Rome in 1972, the authors had tried to predict the situation of the world after 100 years using the World Model. The World Model was based on an SD model and it considered the world population, industrial investment, utilization of natural resources and environmental pollution. Unfortunately, people only expected and criticized the reported numerical results themselves, and didn t pay attention to the usefulness of SD as numerical simulation methodology, because there was little consideration for the limitations and problems of large-scale simulation in social science at that time. The development of software easy to use on personal computers with graphical interface (e.g., STELLA, Vensim) has contributed to spread the utilization of SD in the 1980s. Recently, SD has attracted attention as a tool for system characteristics investigation rather than for prediction based on numerical simulation. Also, the utilization of SD as a learning tool for system thinking in elementary and secondary schools is spreading in Europe and America 1. SD is an effective tool for simulating and analyzing complex systems in which various factors are interrelated and its application range is wide. For example, if you try to analyze an environmental issue, you would build a social model, in which some factors related to ecosystem and human activities are included, focusing on the flows of indicator substances (such as carbon dioxide that is considered as one of the causative factors of global warming). By executing this model under SD, you can grasp the relationship among factors and the flows of indicator substances not only through numerical results but also by visualizing results with graphs. In addition, SD can be used as a tool of decision making and policy examination, because it is easy to compare the results of various scenarios with SD models. For example, Liu et al. [1] have developed a nitrogen cycle model for the system integrating beef cattle production with rice cultivation. They have assessed several scenarios using STELLA for recycling by-products of rice (rice straw) and livestock waste (animal manure) coming from each sector of rice cultivation, beef cattle production and extra nitrogen pool. They showed that the re-circulating production type as well as the complex type of re-circulating rice paddy and forage fields is superior to the ordinary production type in regard to reducing emissions of total nitrogen, increasing manure restoration rate and elevating feed self-sufficiency rate. Thus, SD is also applied to the analysis of actual production system. 1 Massachusetts Institute of Technology has been developing the Institute of Technology System Dynamics in Education Project ( whose Road Maps provide a detailed explanation on SD from its basics. These materials are very useful for beginners to learn about SD.

2 Chapter 3: System Dynamics To develop the analysis models of social systems using SD, it is important to collect useful information as much as possible. Especially, observation and description techniques outlined in Chapters 1, 2, 4 and 5 are useful as means of gathering information for the analysis of social systems on environmental issues. If you want to develop a conservation system for endangered marine animals, for example, it is necessary to obtain behavioral and ecological information about target animals. In this case, means of information gathering such as bio-telemetry are effective. If you want to develop a local environmental conservation system for, it is necessary to obtain information about the state of the forest and land use in the region using remote sensing and GIS techniques. If you want to include the human awareness and activity into the system, the knowledge obtained from human-sensing and ethnography will be a good reference for developing the model. As seen above, observations and descriptions on the field are required as means of information gathering to develop the analysis model. At the same time, simulation with SD can be a method of observation of the system's behavior along a time scale. Observing the state of factors and the changes of relationship between them in the model is useful to find the problems in the system. Furthermore, SD simulations can also be used to predict future situations. As previously mentioned, SD was used to predict 100 years ahead the change of world population, the trend of industrial investment, the utilization of natural resources and the environmental pollution in Forrester's World Model. In this chapter, we use STELLA (isee systems, inc.) to execute the examples and describe the models. STELLA is one of the most popular SD application software. STELLA supports a very intuitive graphical user interface so that beginners can easily use to learn about SD. Vensim 2, software free for educational use, has equivalent functions to STELLA. The description of these software products and an introduction to SD are available from Road Maps in the System Dynamics in Education Project stated in the footnote 1 as well as in the references listed at the end of this chapter. 3.2 Stock, Flow, Converter A system model in SD is described by stock, flow and converter. SD is the leading technique to observe and predict the change of state of elements and the flows of objects and information among elements along a time scale. A stock can be thought as a container where something is stored. A flow can be thought as a valve which controls the inflow to or the outflow from a stock. A converter, which is another element distinct form stocks and flows, is used for defining the auxiliary variables and constants. A suitable model for understanding the concepts of stocks and flows is the bathtub model, which consists of a bathtub, a faucet and a drain and is presented in many introductory books to SD. The state (water volume) in the bathtub changes constantly according to the relationship between the inflow rate from the faucet and the outflow rate to the drain. As such, the bathtub corresponds to a stock. The term level may be often used instead of stock. The faucet and the drain correspond to flows because the inflow rate from the faucet and the outflow rate to the drain changes the state (water volume) of the bathtub. The term rate is often used instead of flow. In this chapter, we will use the terms stock and flow according to the definition of STELLA. Figure 3-1 shows the symbols for stocks, flows and converters, which are used in this chapter. Stock Flow Converter Figure 3-1 Symbols representing a stock, a flow and a converter Figure 3-2 shows the diagram of bathtub model. The symbols described on the left side of the flow faucet and on the right side of the flow drain represent the model boundaries. 2 Available from the website at

3 Faucet Bathtub Drain Figure 3-2 Bathtub Model In order to execute SD using the created model, you need to set concrete values to stocks, flows and converters as well as relational equations between them. For such settings, data collected from statistics or observations are usually used. However, abstract values and relational equations can be used for conceptual models as explained in Section 3.4. For example, if we execute this Bathtub model with the flow Faucet = 5 liters/minute, the flow Drain = 4 liters/minute, the initial value of stock Bathtub = 0 liters and time interval (dt) = one minute, the stock Bathtub will increase by one liter every minute. This relationship can be described in SD as Equation 3-1. Bathtub (t) = Bathtub (t dt) + (Faucet Drain) dt (Equation 3-1) Where t represents time and dt a time interval. In the case of STELLA, if you only connect the stock and flows as shown in Figure 3-2, an equation such as Equation 3-1 is automatically generated. 3.3 Feedback Loop In SD, the flow of information among elements can be described by connecting stocks and flows to one another with connectors. Furthermore, these connecters enable you to easily create models that include feedback loops. At first, we will explain the structure called positive feedback loop by a so-called saving model based on a compound interest. The system diagram of this model is shown in Figure 3-3. The model shown in Figure 3-3 consists of three elements: Deposit Account (stock), Interest Income (flow) and Interest Rate (converter). These elements are connected to each other by connectors. A connector is used to indicate the flow of information from one element (source) to another (destination) using an arrow. Unlike in the Bathtub model in which we have directly set the flow Faucet to a static numerical constant (5 liters/minute), here in the model as shown in Figure 3-3, we set the flow Interest Income to the equation Deposit Account Interest Rate. We set the value of the converter Interest Rate to 0.05 and the initial value of the stock Deposit Account to 10,000. Interest Income Deposit Account Interest Rate Figure 3-3 Saving model based on compound interest. The equation for the stock Deposit Account in Figure 3-3 will be as shown below in Equation 3-2. Deposit Account (t) = Deposit Account (t dt) + Interest Rate dt (Equation 3-2)

4 Chapter 3: System Dynamics When we set the time interval (dt) to one year and run this model, the change of stock Deposit Account up to two years later is as follows: After one year, Deposit Account (1) = Deposit Account (1-1) + Interest Income 1 = Deposit Account (0) + Interest Income Interest Income = the state of stock before update Interest Rate = Deposit Account 0.05 = 10, = 500 Therefore, Deposit Account (1) = 10, = 10,500 Two years later, calculating in the same way, Interest Income = 10, = 525 Deposit Account (2) = Deposit Account (1) + Interest Income = 10, = 11,025 Thus, the increase in the value of stock will cause the value of inflow to rise. As a result, the value of stock in turn increases. Such a relationship is called positive feedback loop. Next, we will explain the structure called negative feedback loop by a Bathtub model with a desired level shown in Figure 3-4. Faucet Bathtub Water Level Difference Desired Level Figure 3-4 Bathtub model with desired level We set the value of converter Desired Level to be 100 liters and the initial value of stock Bathtub to be 0 liters. We redefine convert Water Level Difference to be Water Level Difference = Desired Level Bathtub and the flow Faucet to be Faucet = Water Level Difference 0.4. In this model, the difference between Desired Level and the water volume in Bathtub is calculated and 40% of this value is added to the stock Bathtub through the flow Faucet. When we set the time interval (dt) to be one minute and run this model, the change of stock Bathtub up to two minutes later is as follows: After one minute, Bathtub (1) = Bathtub (0) + Faucet Water Level Difference = Desired Level Bathtub (0) = = 100 Faucet = Water Level Difference 0.4 =

5 = 40 Therefore, Bathtub (1) = = 40 Two minutes later, calculating in the same way, Water Level Difference = = 60 Faucet = = 24 Bathtub (2) = Bathtub (1) + Faucet = = 64 The behavior of model in Figure 3-4 is different from that of model in Figure 3-3. Water level difference is constantly getting smaller and smaller by every minute. As a result, water level in the bathtub gradually approaches the desired level because the increase rate of the stock is reduced. Such a feedback loop is called negative feedback loop. The simple models in Figure 3-3 and 3-4 are examples of monotone change. There are some cases in which a change to the opposite direction is only brought about under a special condition. If such reactions occur, the behavior as a whole gradually converges to the equilibrium but the trend sometimes shows cyclic change or an oscillatory behavior partially. If multiple stocks, flows and converters are connected by connectors, there may be multiple feedback loops in the model. In such a model, a loop starts at stock, goes through some converters of flows, and eventually comes back to the starting stock. The behaviors of stocks or flows sometimes show an S-Shape 3 or cyclic changes according to the combination of positive and negative feedback loops. 3.4 Example: A local development model making efficient use of a rich natural environment Let's make a model using the scenario shown bellow and run it in SD Scenario Assume that agriculture and tourism are the main local industries in the target region A making efficient use of its rich natural environment. Tourists visiting the region A are looking forward to the various activities available in this rich natural environment. So, tourism significantly contributes to the local development of the region A. Also, resort development is carried out to promote the vitality of the local economy in this region by attracting tourists. However, overdevelopment results in environmental destruction, and the greater the number of visiting tourists, the more strain the natural environment has to sustain. For these reasons, the more the rich natural environment is damaged, the less the attractiveness for tourists is, and the less the number of visiting tourists are. As a result, the region vitality will decrease. So, we try to consider the relationship among Rich Natural Environment, Tourist Attractiveness and Region Vitality using SD. First, we consider a rough causal loop diagram based on the above scenario. On top of Rich Natural Environment, Tourist Attractiveness and Region Vitality, we include Sightseeing Load, which represents the increase in the environmental load by increase in visiting tourists, and Resort Development for attracting tourists in the model. Among these elements, we set the following assumptions: The increase of Region Vitality stimulates the efforts of preservation of the natural environment. The increase in Tourist Attractiveness results in the increase in Region Vitality results. The increase in Rich Natural Environment result in the increase in Tourist Attractiveness. 3 Logistic curve is a typical example of S-shaped curves. In a logistic curve, positive feedback loops are dominant before the inflection point, while after negative feedback loops are dominant after the point.

6 Chapter 3: System Dynamics The causal loop diagram based on these assumptions is shown in Figure 3-5. Two elements linked by a double-headed arrow are related each other. On the other hand, a single-headed arrow connecting two elements indicates a unidirectional relationship. The plus sign (+) beside an arrow indicates that these two elements have a positive feedback (both elements change in the same direction). The minus sign ( ) indicates that these two elements have a negative feedback (changes in these elements are in opposite directions). For example, the increase in Rich Natural Environment results in the increase in Tourist Attractiveness and that increase promotes the increase in Region Vitality in turn. The increase in Region Vitality induces the increase of Rich Natural Environment as a result. On the other hand, since both Sightseeing Load and Resort Development have negative feedback to Rich Natural Environment, the increases in these two factors result in the decrease of Rich Natural Environment. Thus, Rich Natural Environment, Tourist Attractiveness and Region Vitality do not always change in the same direction because of the inclusion of negative feedback in the model. Rich Natural Environment + - Sightseeing Load - Resort Development + + Tourist Attractiveness + Figure 3-5 Causal loop diagram + Region Vitality Basic model based on a scenario Let's try to construct a SD model using the causal loop diagram shown in Figure 3-5. First, we must determine stocks, flows and converters. We set Rich Natural Environment, Tourist Attractiveness and Region Vitality as stocks because these elements change along a time scale. Sightseeing Load and Resort Development are assumed to be convertors because these elements are constants impacting the state of stocks. The SD model based on Figure 3-5 is shown in Figure 3-6. The content of each stock, flow and convertor must be defined before running the simulation using SD for the model shown in Figure 3-6. Since Rich Natural Environment, Tourist Attractiveness and Region Vitality are abstract concepts, we assign 50 units as the initial values for these stocks. In this context, unit is a fictitious unit system. If one of the factors, Rich Natural Environment, Tourist Attractiveness or Region Vitality, reaches over 50 units, it is considered to be in a desirable state, and in an undesirable state up to that point. The magnitude of this fictitious unit system has a mathematical meaning. For example, if the value of the stock Rich Natural Environment increases from 50 to 60 units, we can consider that Rich Natural Environment has gained 10 units.

7 Increase Richness Rich Natural Environment Decrease Richness Tourist Attractiveness Sightseeing Load Increase Attractiveness Decrease Attractiveness Region Vitality Resort Development Increase Vitality Decrease Vitality Figure 3-6 SD model The inflow to Rich Natural Environment (Increase Richness) is defined as depending on the state of Region Vitality. We assume that if Region Vitality is more than 50 units, people are more interested in the preservation of the natural environment and it contributes 10 units to the increase of Rich Natural Environment, while it is less than 50 units, people cannot make efforts for the preservation of the natural environment. We assume that the outflow from Rich Natural Environment (Decrease Richness) is determined by two convertors, Sightseeing Load and Resort Development. That is, if the sum of Sightseeing Load and Resort Development becomes positive, the natural environment is negatively impacted. So, we define that Rich Natural Environment is decreased by 15 units. We assume that both the inflow to Tourist Attractiveness (Increase Attractiveness) and the outflow from it (Decrease Attractiveness) depend on Rich Natural Environment. Tourists are interested in the rich natural environment in Region A, so Rich Natural Environment directly affects Tourist Attractiveness. Therefore, if the state of Rich Natural Environment is more than 50 units, the value of the flow Increase Attractiveness will be 10 units, while it is less than 50 units, the value of the flow Decrease Attraction will be 15 units. Both the inflow to Region Vitality (Increase Vitality) and the outflow from it (Decease Vitality) are assumed to depend on the state of Tourist Attractiveness. If the state of Tourist Attractiveness is more than 50 units, the value of the flow Increase Vitality will be 15 units, while it is less than 50 units, the value of the flow Decrease Vitality will be 15 units. The convertor Resort Development is defined as 1 unit if both Tourist Attractiveness and Region Vitality are more than 50 units. We assume that the motivation to develop resorts is enhanced not only when many tourists are visiting the region, that is, the tourist attractiveness is high, but also when the vitality in the region is enough. On the other hand, the convertor Sightseeing Load is defined as 1 unit if Tourist Attractiveness is more than 50 units. Equations describing the model defined above are shown in Figure 3-7. These equations cannot be input directly in STELLA. Setting these equations is done by using the Model mode in STELLA. In this mode, you can click every stock, flow and convertor to set their equations using the input dialog displayed in STELLA. Run the simulation by SD after setting the equations for the model. We run the model for 20 years. Stocks are updated every year (i.e. the value of t is 0 =< t =< 20 and dt = 1 in the equations described in Figure 3-7). The changes of three stocks, Rich Natural Environment, Tourist Attractiveness and Region Vitality are shown by the graph in Figure 3-8.

8 Chapter 3: System Dynamics Rich Natural Environment (t) = Rich Natural Environment (t dt) + (Increase Richness Decrease Richness) dt Initial value: Rich Natural Environment = 50 Inflow: Increase Richness = if (Region Vitality >= 50) then (10) else (0) Outflow: Decrease Richness = if ((Resort Development + Sightseeing Load) > 0) then (15) else (0) Tourist Attractiveness (t) = Tourist Attractiveness (t dt) + (Increase Attractiveness Decrease Attractiveness) dt Initial value: Tourist Attractiveness = 50 Inflow: Increase Attractiveness = if (Rich Natural Environment > = 50) then (10) else (0) Outflow: Decrease Attractiveness = if (Rich Natural Environment <50) then (15) else (0) Region Vitality (t) = Region Vitality (t dt) + (Increase Vitality Decrease Vitality) * dt Initial value = 50 Inflow: Increase Vitality = if (Tourist Attractiveness > =50) then (15) else (0) Outflow: Decrease Vitality = if (Tourist Attractiveness < 50) then (15) else (0) Resort Development = if ((Tourist Attractiveness >= 50) AND (Region Vitality >= 50)) then (1) else (0) Sightseeing Load = if (Tourist Attractiveness >= 50) then (1) else (0) Figure 3-7 Equations for the model in Figure 3-6

9 unit year Figure 3.8 Changes in each stock : Rich Natural Environment : Tourist Attractiveness : Region Vitality During the first year, since both Tourist Attractiveness ( ) and Region Vitality ( ) are 50 units, which is their initial value (value at year 0), both Resort Development and Sightseeing Load are 1 unit and so, Increase Richness is less than Decrease Richness, resulting in that the value of Rich Natural Environment is decreased by 5 units. During this period, both Tourist Attractiveness and Region Vitality increase. While both inflow and outflow of Region Vitality are 15 units, the inflow of Tourist Attractiveness is 10 units and its outflow is 15 units. Tourist Attractiveness is more sensitive to the decrease of Rich Natural Environment than Region vitality because the decrease rate is greater than the increase rate due in relation to Rich Natural Environment. As a result, the decrease of Tourist Attractiveness occurs earlier than the decrease of Region Vitality. The increase and decrease of Region Vitality is directly affected by Tourist Attractiveness alone, and only indirectly by the increase and decrease of Rich Natural Environment, being mediated by Tourist Attractiveness. In this model, the delayed response of Tourist Attractiveness and Region Vitality is induced by the increase and decrease of Rich Natural Environment. So, every stock repeatedly rises and falls during 20 years. The expression of Increase Richness = if (Region Vitality >= 50) then (10) else (0) is a so-called if-statement. The format of an if-statement is if (condition) then (statement or value) else (statement or value). If the condition is true, the statement or value in the then block is selected, while, if it is false, the else block is selected. For example, a statement Increase Richness = if (Region Vitality >= 50) then (10) else (0) means that Increase Richness is assigned to 10 unit when Region Vitality is more than 50 units, while it is assigned to 0 unit when Region Vitality is less than 50 units. In the case of multiple conditions being used such as Resort Development = if ((Tourist Attractiveness >= 50) AND (Region Vitality >=50)) then (1) else (0), operators such as AND or OR are used. A statement Resort Development = if ((Tourist Attractiveness >= 50) AND (Region Vitality >= 50)) then (1) else (0) means that if and only if both Tourist Attractiveness and Region Vitality are more than 50 units, Resort Development is assigned to 1 unit, and if not, it is assigned to 0 units Comparison among scenarios using SD In the model of Figure 3-6, we assume Region Vitality and Resort Development as the factors affecting Rich Natural Environment and that the flow Increase Richness is always assigned to 10 units when Region Vitality is more than 50 units. In addition, Resort Development only affects Decrease Richness and does

10 Chapter 3: System Dynamics not affect Increase Vitality directly. Results from the simulation using SD under these assumptions have made it clear that the changes in Rich Natural Environment affects Tourist Attractiveness and Region Vitality. Then, let's examine what kind of consideration is possible using SD if you are asked to decide the best balance between the efforts of preservation of the natural environment and the resort development. A simple example is shown as follows: Assume that we will make some efforts for preserving the natural environment to maintain and improve Rich Natural Environment. Though resort development is one of the causes of environmental destruction, it is expected to help local development at the same time, attracting tourists and promoting employment in the region. Therefore, we modify the model of Figure 3-6 by taking into consideration the efforts of preservation of the natural environment and the effects of resort development, to make the model shown in Figure 3-9. In the model of Figure 3-9, we assume that the convertors Preservation Coefficient and Development Coefficient are linked to Preservation Effort and Resort Development, respectively. These convertors give constants (coefficients). When you execute the simulations changing various parameter values in a model, it is useful to define the target parameters as the independent convertors. Even though we don't mention it in this chapter, such kinds of convertors can be handled with Slider or Nob in the interface layer of STELLA. Equations corresponding to Figure 3-9 are shown in Figure Changes in each stock by combinations of Preservation Coefficient and Development Coefficient are shown in Figure We consider four scenarios as follows: (a) No efforts of environment preservation (Preservation Coefficient = 0 units) but with resort development (Development Coefficient = 5 units). (b) Preservation Coefficient is set to 5 units but no resort development (Development Coefficient = 0 units). (c) Both Preservation Coefficient and Development Coefficient are set to 5 units. (d) Preservation Coefficient is set to 15 units and Development Coefficient is set to 5 units. The result of the scenario of resort development without the efforts of environmental preservation shows that Rich Natural Environment becomes 0 units at the fifth year, and both Tourist Attractiveness and Region Vitality temporally increase but decrease rapidly thereafter (Figure 3-11a). In the case where both Preservation Coefficient and Development Coefficient are set to 5 units (Figure 3-11c), the changes in Tourist Attractiveness and Region Vitality show the same behavior as shown in Figure 3-11a. However, Rich Natural Environment exhibits little change and recovers its initial value (50 units) in the 13th year, because Preservation Coefficient is set to 5 units/year in Figure 3-11c. On the other hand, all stocks show cyclic behaviors when Preservation Coefficient is set to 5 units and Development Coefficient is set to 0 units (Figure 3-11b). However, Region Vitality decreases gradually with repeated increases and decreases. When we put a large weight on the environmental preservation (Preservation Coefficient = 15 units, Development Coefficient = 5 units), all stocks show the same cyclic behaviors as in Figure 3-11b but Region Vitality is always greater than its initial value (50 units). Both Rich Natural Environment and Tourists Attentions are oscillating around the initial value (50 units) with the range of ±10 units. By comparing the four results shown in Figure 3-11, we can say that it is important to make efforts to preserve the natural environment but also necessary to develop resorts to a certain extent for promoting the development of the region using its rich natural environment.

11 Increase Richness Rich Natural Environment Decrease Richness Preservation Effort Sightseeing Load Preservation Coefficient Tourist Attractivenes Sightseeing Benefit Increase Attractiveness Decrease Attractiveness Resort Development Development Coefficient Increase Vitality Region Vitality Decrease Vitality Figure 3-9 Model taking into consideration the efforts of environmental preservation and the effects of resort development In this chapter, we considered models with very simple assumptions to present examples of simulation using SD. Though the models shown here is not enough to solve problems of the actual society system, we think they help you to understand the concept of SD and how to construct models. If you expand these models into society models for the development of a region, you need to take into account the following points. You should define the method to evaluate Rich Natural Environment more precisely. For example, you can consider the range of area to preserve or the proper preserving method by classifying the land use of a whole region using remote sensing and by evaluating the changes in natural environment up to the time using the time series data acquired from remote sensing. It is possible to include sightseeing load and effects of resort development more accurately through a more advanced ecosystem-model. With regards to Tourist Attractiveness, it is useful to consider an evaluation index based on dynamic statistics of the number of tourists or doing a questionnaire survey targeting them. In the case of Region Vitality, you can make more detailed models by taking into consideration some kinds of information such as the industrial structure of the region, the age structure of employees, the movement of the population, and the economic index in addition to the information concerning resort development and tourism. In this chapter, we considered models with very simple assumptions to present examples of simulation using SD. Though the models shown here is not enough to solve problems of the actual society system, we think they help you to understand the concept of SD and how to construct models. If you expand these models into society models for the development of a region, you need to take into account the following points. You should define the method to evaluate Rich Natural Environment more precisely. For example, you can consider the range of area to preserve or the proper preserving method by classifying the land use of a whole region using remote sensing and by evaluating the changes in natural environment up to the time using the time series data acquired from remote sensing. It is possible to include sightseeing load and effects of resort development more accurately through a more advanced ecosystem-model. With regards to Tourist Attractiveness, it is useful to consider an evaluation index based on dynamic statistics of the number of tourists or doing a questionnaire survey targeting them. In the case of Region Vitality, you can make more detailed models by taking into consideration some kinds of information such as the industrial structure of the region, the age structure of employees, the movement of the population, and the economic index in addition to the information concerning resort development and tourism.

12 Chapter 3: System Dynamics Rich Natural Environment (t) = Rich Natural Environment (t dt) + (Increase Richness Decrease Richness) dt Initial Value: Rich Natural Environment = 50 Inflow: Increase Richness = Preservation Effort Outflow: Sightseeing Load + Resort Development Tourist Attractiveness (t) = Tourist Attractiveness (t dt) + (Increase Attractiveness Decrease Attractiveness) dt Initial Value: Tourist Attractiveness = 50 Inflow: Increase Attractiveness = if (Rich Natural Environment >=50) then (10) else (0) Outflow: Decrease Attractiveness = if (Rich Natural Environment <50) then (15) else (0) Region Vitality (t) = Region Vitality (t dt) + (Increase Vitality Decrease Vitality) dt Initial Value: Region Vitality = 50 Inflow: Increase Vitality = Sightseeing Benefit +Resort Development Outflow: Decrease Vitality = if (Tourist Attractiveness < 50) then (10) else (0) Resort Development = if ((Tourist Attractiveness > 40) then(development Coefficient) else (0) Sightseeing Load = if (Tourist Attractiveness >= 50) then (5) else (0) Preservation Effort = if (Rich Natural Environment < 50) then(preservation Coefficient) else (0) Sightseeing Benefit = if (Tourist Attractiveness >= 50) then (10) else (0) Development Coefficient = 5 Preservation Coefficient = 5 Figure 3-10 Equations for the model in Figure 3-9

13 (a) (b) 自然環境の豊かさ観光魅力度地域活力度 自然環境の豊かさ観光魅力度地域活力度 unit 40 unit (c) 年 (d) 年 unit 自然環境の豊かさ観光魅力度地域活力度 Figure 3.8 Evolution of each stock unit 自然環境の豊かさ観光魅力度地域活力度 年 年 Legend : Rich Natural Environment, : Tourists Attractiveness, : Region Vitality Top left (a): Preservation Coefficient = 0 units, Development Coefficient = 5 units Top right (b): Preservation Coefficient = 5 units, Development Coefficient = 0 units Bottom left (c): Preservation Coefficient = 5 units, Development Coefficient = 5 units Bottom right (d): Preservation Coefficient = 15 units, Development Coefficient = 5 units References 1. Liu Chen, Tetsuhiko Yoshimura, Kazuyuki Moriya and Tetsuro Sakai: A simulation of beef cattle production integrated with rice cultivation using system dynamics (in Japanese), Bulletin of Beef Cattle Science, 72, pp (2002). 2. Morita Michiya edit.: Keiei System no Modeling Gakusyu STELLA niyoru System Thinking [Leaning about Administration Systems Modelling System Thinking Using STELLA], Makino Shuppan (2001). 3. Tsuchikane Tatuo: Simulation niyoru System Dynamics Nyumon [Introduction of System Dynamics by Simulation], Tokyo Denki Daigaku Syuppannkyoku [Tokyo Denki University Press] (2005). 4. Barry M. Richmond: Introduction to System Thinking I Education (in Japanese), VarsityWave trans., CUTT System Development Laboratory (2004). 5. Barry M. Richmond: Introduction to System Thinking II Business (in Japanese), VarsityWave trans., CUTT System Development Laboratory (2004). (Kazuyuki Moriya)