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Introduction
Introduction
The goal of systems dynamics approach to modeling complex systems is to describe the complexities using stock, flows and feedback loops. Not all inputs are flows, for example a constant perturbation in an otherwise decaying system is considered to have only one flow that is the net diffrence between the constant and decay term i.e. a goal seeking dynamics where the systems chases the goal and once reached stays there (a stable equilibrium).
dE/dt=(E0-E)/RAT
E0 is the goal (equilibrium) E is the expected sales stock. There is only an inflow that adjusts to the goal, there are no inflow and outflow. A stock flow diagram is shown in Figure 1.
Other basic dynamical behaviors such as exponential growths (uncontrolled growth), goal seeking dynamics, S-shaped (growth with constrains), Oscillatory, growth with overshoot, overshoot and collapse together with time delays form the building blocks in many complex systems ranging from service industry to population growth.
Fig 1. (upper panel) A stock flow diagram for expected sales dynamics as it tries to achieve the 'Actuals Sales' goal. (lower panel) A feedback loop formed by the goal seeking behavior, a so called balancing loop.
Exponential Growth
Exponential Growth
Exponential growths occur where the rate of increase of a stock is proportional to the value of the stock at the current moment. Example of sucha growth is uncontrained population growth.
Oscillatory goal seeking dynamics
Oscillatory goal seeking dynamics
Oscillatory goal seeking patterns arise when there is a delay in reacting to the goal so that the target value of the stock is always overshot, where the stock shoots either above or under the goal due to delayed adjustmnet. An example is temperature oscillatoions due to delays in thermostat.
dT/dt=(target temperature-T(t-tau))/TAT
Sigmoidal growth: Constrained population growth
In real life growth cannot happen in an uncontrolled fashion. IT is ultimately limited by the carrying capacity of the environment. This realitly is often modeled as a sigmoidal growth.
dP/dt=birht rate* P - death rate P*P/Carrying capacity
Overshoot and Collapse
Overshoot and Collapse
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