Understanding System Equilibrium, Feedback Loops, and Delays

What is Equilibrium in a System?

Equilibrium in a system refers to a state of balance. It's the point around which the system is linearized. At equilibrium, the system's variables remain constant, meaning their time derivatives are zero.

Negative feedback mechanisms are crucial for maintaining equilibrium. They counteract changes and stabilize the system. For example, an increase in a variable triggers a response that decreases that variable.

Example: If the temperature in a room increases, the thermostat activates the air conditioning, eventually leading to a decrease in room temperature back to its initial value.

Positive Feedback Loops and Exponential Growth

The characteristic behavior of a positive feedback loop is exponential growth. This means that for each time interval, a value in the level doubles.

The exponential growth of an accumulator (level) is characterized by a doubling time constant. The time it takes to double its value for a simple positive feedback loop can be approximated as follows:

Doubling Time = 0.7 / Factor Growth

Negative Feedback Loops of the First Order

Feedback is considered negative if an increase in one variable causes a subsequent decrease in the same variable. Negative feedback loops tend to balance or stabilize systems, resulting in asymptotic or oscillating behavior. The system converges asymptotically towards a target value. For example, market saturation, where the level is the market for the product and the flow is sales.

Exponential decay is a common behavior in negative feedback loops. An important feature of exponential decrease is its asymptotic behavior, where the value of the level approaches a target level and remains constant. The "halving time" is the time it takes for the variable to reduce by half.

Problems with Causal Loop Diagrams

According to George P. Richardson, causal loop diagrams have limitations. Their structure doesn't clearly differentiate between levels and flows, unlike level and flow diagrams, which are less ambiguous.

The primary issue is that causal loop diagrams lack the clarity needed to understand the defining characteristics of a system's structure and behavior. The recommended solution is to use stock-and-flow diagrams to model the system directly, bypassing causal loop diagrams.

Generic Structures in System Dynamics

Generic structures are common patterns found in various systems.

A generic structure can be applied to different environments, facilitating learning by enabling knowledge transfer. It allows for estimations of the behavior of new systems based on already known structures. For example, in an ecological system, an increase in the deer population leads to more deer being born. This structure can be transferred to other systems, such as a bank account where deposits lead to more money.

Understanding Delays in System Dynamics

A delay refers to the time required for a change in variable X to have an effect on variable Y. Delays always involve some form of accumulation (material or information).

First-Order Delays: Characterized by a level that absorbs the difference between the rate of entry and exit.

Third-Order Delays: Characterized by three levels connected sequentially, where the output of the first level becomes the input of the second, and the output of the second becomes the input of the third. Similar to first-order delays, they absorb the difference between the input and output rates.