Fixed Points & Stability: the Test |f′(x*)| < 1
This lesson is part of the course
In this lesson
You find the fixed point of the logistic map for six growth rates, compute the slope there, decide with IF and ABS whether it is stable and estimate how fast the orbit settles.
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Lessons in this course
- Iterating a Function: Recurrences Copied Down & the Cobweb Idea Locked
- Fixed Points & Stability: the Test |f′(x*)| < 1 Locked
- The Logistic Map for Different r: Convergence, a 2-Cycle & Chaos (with a Chart) Locked
- Period Doubling & a Bifurcation Table: Long-Run Values for Each r Locked
- Sensitive Dependence: Two Starting Points a Millionth Apart Locked
- The Lyapunov Exponent: Averaging ln|r(1 − 2x)| Along an Orbit Locked
- Population Models: the Ricker Map, Oscillations & Harvesting Locked
- Mandelbrot & Julia Sets: Escape-Time Counts, an Area Estimate & a Colour Scale Locked