Section 1.7: Problem 18

To explore the dynamics of several excercises using Phaser, we added the following general cubic map as a new Custom equation to Phaser's Custom Equation Library. Please consult the Phaser tip Adding Equation. Just change the values of the parameters a, b, c, and d, to get the map you want.

 


A general Cubic 1D MAP as entered into Phaser's Custom Equation Library.

 


StairStep diagram and two solutions of the cubic map for a = 1, b = 1, c = 1, d = 0.

  • Click on the picture above to load it into your local copy of Phaser. Enter several more initial conditions near the origin using the left mouse button. Clear and Go.
  • Change the value of the parameter b to -1 to explore Exercise 19. (PhaserTip: Parameters) Clear and Go. What happened to the stability type of the origin?



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