Brief Tutorial on Dynamic Systems

From The Origin of Wealth by Eric D. Beinhocker:

A dynamic system is one that changes over time.

When scientists talk about a system being dynamic, what they mean is that the state of the system at the current moment is a function of the state of the system at the previous moment, and some change in between the two moments.

A simple example of a dynamic system is a bank account. The state of the account, or balance, changes over time. Your balance tomorrow is dependent on your balance today, plus any changes during the intervening day, such as deposits, withdrawals, or interest payments.

Changes in dynamic systems can either be discrete, like a bank account, in which the changes occur at specific points in time (e.g. interest is paid on a particular day), or they may be continuous and smooth, like the orbiting of planets.

A convenient way to describe a dynamic system is in terms of stocks and flows. A stock is an accumulation of something, such as the balance in a bank account. The rate at which a stock changes over time is known as a flow, for example, the rate of money flowing into or out of a bank account.

In an economy the various stocks and flows are connected to each other in complex ways. For example, if the stock of employment fell to a low level, a policy maker might decide to cut interest rates in order to encourage borrowing, which would expand the stock of money available for investment, which would then be used by businesses to invest in new productive capacity, creating demand for employees, thus raising the stock of employment, which finally would feed back to affect future interest rate policy. Such chains of relationships between stock and flows in a dynamic system are known as feedback loops.

Feedback occurs when the output of one part of a system is the input for another, so, for example, A affects B, which affects C, which comes back to affect A again.

Positive feedback occurs when the connections are reinforcing – if I push A, it pushes B even harder, which pushes C even harder, which pushes A harder than my original push, and so on.

Despite the word positive in the phrase, downward spirals are also a form of positive feedback. For example, a drop in consumer confidence can lead to decreased spending, which leads to decreased production, which leads to unemployment, which leads to even lower consumer confidence and thus a further drop in spending, spiraling right down into recession.
The key thing to remember is that positive feedback reinforces, accelerates, or amplifies whatever is happening, whether is it a virtuous cycle of a downward spiral.

The opposite is negative feedback. Negative feedback is a dampening cycle – instead of reinforcing, it pushes in the opposite direction. While positive feedback accelerates change, negative feedback dampens change, controls things, and brings things back in line.

Dynamic systems also have a third ingredient – time delays. You have probably had the experience of taking a shower in an unfamiliar place such as a hotel, turning on the hot water, noticing it isn’t hot enough, turning it up some more, and then it turns scalding, so you turn it down, it is still too hot, so you turn it down some more, then it is freezing, and so on. The problem is that there is a small time delay between your actions on the water knob and the feedback from the shower temperature. The delay causes you to overshoot and oscillate around the desired temperature. Eventually you figure it out and the oscillations get smaller and smaller until you hit the desired temperature. The longer the time delay, however, the harder it is to control the shower and the more oscillations you get.

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