Basic building blocks of SD Levels (Stocks), Rates (Flows), Auxiliary variables and Arrows Essential building blocks Represent the way dynamic systems really work

The LEVEL Levels represent accumulations (physical and non-physical). Levels represent the ‘traces’ left by activities. The material in a stock exists at a point in time. Stock - level persist when activities cease. Examples: water, predators, CO 2, frustration, knowledge, vegetation,….

The RATE Rates represent activities or actions. Rates occur over time. Rates: Fill and drain stocks Transport staff (physical and non-physical) Can change ‘instantaneously’ Examples: eating, learning, runoff, communicating,….

The RATE ‘infinite’ source spigot ‘infinite’ sink conduit flow regulator direction of flow

Example

Arrows Radiate signals that serve as inputs to decisions or actions. Arrows serve as inputs, rather than inflows, and outputs, rather than outflows. They link stocks and flows (and flows to flows), in order to generate actions.

Auxiliary variables They modify the activities (within the system) They transform inputs into outputs They represent information or material quantities They break out the detail of the logic They do not accumulate (their value is re- calculated in each time step) They can be used for external inputs

Example Causal loop of natural resources and usage Level – natural resources Rate - usage

Example

System Principle 2 Levels and rates are the primary components of the structure. System Principle #1 states that feedback loops are the building blocks of systems. In the same way, levels and rates are the building blocks of feedback loops.

Exercises Everything around us can be represented by either a level (stock) or a rate (flow).

System Principle 3 Do not be fooled by units Units do not determine whether a variable is a level or a rate.

Exercises What are some of the flows that might be associated with the various stocks below? What are their units?

Exercises

buying rate selling rate units # of computers/day #of computers # of computers/day

Exercises

growth rate cutting rate units # of trees per year #of trees # of trees per year

Graphical integration Bathtub example A. Open faucet permanently, 2 L/min Constant Positive rate after 2 min, 2 min * 2 L/min = 4 L after 6 min, 6 min * 2 L/min = 12 L

Graphical integration

B. Step function

Graphical integration

C. Linearly increasing flow

Graphical integration

Key Ideas: When the net flow is positive, stocks are filled; when the net flow is negative, stocks are emptied. The area under the flow graph over the period of time is equal to the change in the value of the stock over that same time period. Final value of stock = Initial value of stock + Area under flow graph Linearly increasing flows cause the stock to exhibit parabolic growth. Linearly decreasing flows cause the stock to exhibit decreasing parabolic behavior. Complex graphs can be broken down into several smaller, simpler ones.

SD Modeling Process Define the issue/problem Develop & Represent Hypotheses Test Hypotheses Design and Test Policies Challenge the Boundaries Make Learning Available

SD Modeling Process 1.Define the Issue / Problem a. Explicitly state the purpose b. Develop a reference behavior pattern c. Develop a system diagram 2.Develop& Represent Hypotheses a. Seek a dynamic organizing principle b. Map the hypotheses c. Make the map simulatable

SD Modeling Process 3.Test Hypotheses a. Mechanical mistake tests b. Robustness tests c. Reference behavior tests 4.Design & Test Policies a. Policy tests b. Sensitivity tests c. Scenario tests

SD Modeling Process 5.Challenge the Boundaries a. Extensive boundary b. Intensive boundary 6.Make Learning Available a. Develop a drama b. Design a learning process c. Implement the progression d. Create in-character feedback and coaching sequences

Simulation structure and behavior Move from casual loops to flow diagrams is done to provide additional insight into the behavior of a proposed model over time. The strategy in forming a model: 1. start with a causal loop diagram 2. formulate a flow diagram 3. write equations 4. use the equations to simulate the model on the computer Once a model is developed we can use it to explore the consequences of alternative model assumptions and proposed policy interventions.

Example World population growth Assumption - constant growth (percent per year) of GF 2% / year.

Example Causal loop Net Births = Number of newborns – Number of dead [people/year]

Example Stock and flow diagram

Example Equations Rate function for Net Births NB = POP(T) * GF Level equation for Population POP(T) = POP(T-1) + DT * NB where DT is time interval = 1 year Complete Model consists of two equations: NB = POP(T) * GF POP(T) = POP(T-1) + DT * NB NB depends on the size of the population POP. POP varies over time. So NB should have a time subscript too. What should be used?

Example Try out hand simulation. DT = 1 year, start with in T = 1975 POP(T) = 4 billion NB = POP(T) * GF = POP(1975) * GF = 4 * 0.02 NB = 0.08 billion per year in 1976 POP(1976) = POP(1975) + DT * NB = * 0.08 = 4.08 billion So, NB for 1975 to 1976 is calculated using 1975 NB(T, T+1) = POP(T) * GF Final model for world population: NB(T,T+1) = POP(T) * GF POP(T) = POP(T-1) + DT * NB(T-1,T)

Example

System Principle 4 Levels accumulate the results of rates (actions) in the system.