Period Doubling Route to Chaos in a Discrete Population Model Difference Equation

Numerical Analysis, Class 6B

#PeriodDoubling #ChaosTheory #mathematica

Links and resources
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(0:00) Fish population density
(3:47) Discrete difference equation model (based on a parameter k)
(5:33) One goal: solve for pn in terms of p0
(7:04) Main goal: experimentally observe what happens under iteration as k increases
(8:48) What function gets iterated with NestList in Mathematica?
(9:45) Review the logistic map example fixed points
(11:15) The new example has fixed points at 0 and 1
(12:25) Stability analysis (use the derivatives at the fixed points)
(15:45) Exploration with Wolfram Mathematica
(20:54) Observe period doubling
(25:47) Chaotic behavior
(28:31) Beautiful animation of the cobweb plot as k changes
(30:40) Period doubling route to chaos and bifurcation diagrams
(41:20) First Feigenbaum constant (a universal constant)
(43:07) Summary of bifucation diagram

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