Linear systems behave nicely - whenever you slightly increase the input, the output also increases only by a small amount. Thus linear systems are quite easy to predict. You can make small errors in measurements of your inputs, which will have almost no impact on the accuracy of your prediction.

Nonlinear systems are different in this regard - even small difference in the input can lead to divergent outputs. In other words the differences between the systems trajectories, or alternatively differences between your prediction and the actual behavior of the system, won't be noticeable at first, but with time those small differences will get amplified. Typical example being weather, where tomorrows forecast are likely to be more reliable than 7-day forecast.

More nonlinear systems, dynamical chaos and chaos theory in the following video by Seeker. We invite you to watch it.

Today we continue our series of posts on compartmental voter model. Recently I had another idea how to examine the impact of the finite capacity on the compartmental voter model dynamics. And this approach also involves populations dynamics in the model.

For a different approach see the earlier post on the finite capacity in the compartmental voter model.

Today we continue our series of posts on compartmental voter model. Today we ask a question: is there a symmetry between stationary (temporal) and spatial distributions? Note that we have observed this symmetry in the infinite capacity case, but we haven't yet looked from this perspective in the finite capacity case. In this case we just know that we no longer observe the Beta distributions, which we have observed in the infinite capacity case.

In the last post we have introduced you to the compartmental voter model [1]. While we have introduced the concept of capacity and allowed for a brief exploration of it, this time we dig slightly deeper into this topic.

It seems that COVID-19 "wind" has blown on the house of cards, which we have been carefully rebuilding since 2008 crisis. Though the markets are not the economy, but the economy is likely to stall as it did after so many crashes before. We invite you to watch an Extra History episode (by Extra Credits), which provides historical retrospective on The 1929 Crash, which was followed by The Great Depression.

What do you think will our economy fall as the financial markets did?