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FIGURE 2.2
Plot of the Mira curve for a = 0.99. The starting point coordinates are (4, 0). Top panel: b =
1, bottom panel: b = 0.98.

2.8.1 Mira’s Model
The coordinates of the points on the Mira curve are generated iteratively
through the following system of nonlinear difference equations:

xk( + 1 ) = by k( ) + F xk( ( ))
(2.43)
yk( + 1 ) = − x k( ) + F x k(( ( + 1 )))

where

( −
Fx () = ax + 21 ax ) 2 (2.44)
1 + x 2

We illustrate the different morphologies of the solutions in two different
cases, and leave other cases as exercises for your fun and exploration.

© 2001 by CRC Press LLC