Cycles and Patterns in Systems

[effortlesslumen]

Recognizing Systems is easy in comparision to unrevealing cycles within those. Is it my way of thinking or that recognizing patterns also involves a direct experience of trial and error, which can only be unterstood by experience and learning and observation. The loops within a simple system can easily be  recognized, but not so easily with complex linear or nonlinear ones. The only efficent way for recognizing cycles and patterns in systems i can think of right  now is gathering a lot of information. Is there a better way for seeing and understanding cycles?

And yes, i have watched leos videos on this topic.

 

Here are my own rather unintelligent quick thoughts i had when writing this question:

 

 

Edited August 29, 2023 by effortlesslumen

[LastThursday]

Use maths.

The very basic behaviours of systems are either damping, exponential (growth) or oscillation. All of these are tied to solutions of differential equations. Essentially it boils down to combinations of exponential functions and complex numbers.

The next level is combinations of those, i.e. damped oscillation and so on (think bouncing spring).

Next is chaotic attractors. This is basically oscillation and/or damping with a certain degree of uncertainty or high sensitivity to initial conditions (see chaotic pendulum).

A huge range of systems exhibit the above behaviours. For example animal populations, electric circuits, virus pandemics, planetary motion, bouncing balls, radioactivity, number of bugs in a computer program and so on. Almost all systems are non-linear (i.e. exponential in some way), and you have to work quite hard to make them behave in a linear manner.

Whenever you get two opposing exponential processes, you tend to get oscillation. If one of the processes wins out, you get damping or runaway exponential growth.

In practice unbounded exponential growth is not possible and usually some opposing process will stop it - and you will get the well known S shape. This happens in pandemics, animal populations and Moore's law in chip transistor density.

And there ends my engineering lesson.

Edited August 29, 2023 by LastThursday