# Nonlinear Systems-6 Exponentials & Power Laws

Exponentials are a signature key of nonlinear systems, unlike linear growth exponential grow represents a phenomenon where the actual rate of growth is growing itself to generate an asynchronous development with respect to time and some very counter-intuitive events. In this module we will discuss the dynamics of exponentials and their counterparts power laws that represent a power relation between two entities.

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Transcription excerpt:

Part of our definition for linear systems is that the relationship between input and output is related in a linear fashion, the ratio of input to output might be 2 times as much, 10 times as much or even a thousand times it is not important this is merely a quantitative difference, what is important is that this ratio between input and output is itself not increasing or decreasing. But as we have seen when we have feedback loops the previous state to the system feeds back to effect the current state thus enabling the current ration between input and output to be greater or less than its ratio previously and this is qualitatively different.

This phenomenon is captured within mathematical notation as an exponential. The exponential symbol describe how we take a variable and we times it by another not just once but we in fact iterate on this process, meaning we take that output and feed it back into compute the next output, thus the amount we are…

- Kind: Short
- Year: 2015
- Runtime: 5 min
- By: Complexity Academy
- Genres: Science
- Archive: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Nonlinear_Systems-6_Exponentials_%26_Power_Laws.webm)
- Licence or status: [CC BY 3.0](https://creativecommons.org/licenses/by/3.0) (as the archive states it)
- Credit: Complexity Academy
- Who can watch: Tweens profiles and older (the archive gives no rating; placed by Invisible Network from its collection and subjects)

[Watch now](https://invisiblenetwork.ai/watch/archive/commons/58002321?play=1)