# Nonlinear Systems- 11 Phase Transitions & Bifurcations

A phase transition is the transformation of a system from one state to another through a period of rapid change. The classical example of this is the transition between solid, liquid and gaseous states that water passes through given some change in temperature, phase transitions are another hallmark of nonlinear systems. In this module we discuss the concept in tandem with its counterpart bifurcation theory.

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Transcription excerpt:

Bifurcations & Phase transitions As we have previously discussed the qualitative dynamic behavior of nonlinear systems is largely defined by the positive and negative feedback loops that regulate their development, with negative feedback working to dampen down or constrain change to a linear progression, while positive feedback works to amplify change typically in an super-linear fashion. As opposed to negative feedback where we get a gradual and often stable development over a prolonged period of time, what we might call a normal or equilibrium state of development, positive feedback is characteristic of a system in a state of nonequilibrium. Positive feedback development is fundamentally unsustainable because all systems in reality exist in an environment that will ultimately place a limit on this grown. >From this we can see how the exponential grow enabled by positive feedback loops is what we might say special, it can only exist for a relatively…

- Kind: Short
- Year: 2015
- Runtime: 6 min
- By: Complexity Academy
- Genres: Science
- Archive: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Nonlinear_Systems-_11_Phase_Transitions_%26_Bifurcations.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/58002375?play=1)