Tent Functions And Equation Groups

Do Not Confuse Them With Differential Equations

Thanks to a dear reader of mine, I stumbled over tent maps and groups of equations. Although I never got involved in this matter, my curious mind couldn’t just let it slide. So I began reading about this topic, and the dear reader even sent me a book from America to far-away Germany.

The book is called

A very interesting read, to say the least.
It covers everything from sets to logistic functions and even the chaos theory.
But this is not going to be a book review, no. This is about tent maps, so let us get right into it.

The initial question was whether the following equations describe a differential equation:

Admittedly, it does look like a DE. However, on a second look, both are simple equations that define a graph within a certain interval. They form a line to look like a tent in the interval [0,1].

Alright, now that we know that tent functions are not differential equations, what are they then? And a better question — what are they used for?

Tent maps are part of the overarching topic of dynamics. Generally, dynamics concerns itself with transient problems. That is, systems that change their state throughout a timespan. For example, we could look at a resonant tunneling diode (RTD) and observe what happens when a current flows through it. The current comes from an external power supply, and thanks to the Liouville-von-Neumann equation, we can simulate what happens inside such a double barrier RTD.

What you see above is the carrier density in a double barrier RTD. We can see how the electrons distribute within the device. The blue line represents the steady state with no external supply…

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