# Chaos and Time-Series Analysis

## J. C. Sprott

## Changes for Next Edition

- Include a footnote to the sound file at https://sprott.physics.wisc.edu/chaostsa/fig09-07.wav.
- Include example of attracting 2-torus in 3-space (ref: Henryk
Zawadzki).
- Expand Fig. 10.19 to look like 10.18.
- Say more about catastrophes (see Gottman, et. al. 2002).
- Graph oscillation frequency versus drive frequency for driven
van der
Pol
showing Devil's staircase and mention period adding.
- Expand Chapter 1 with more examples and figures, including
Kiers
circuit.
- Add a section on chaos control and synchronization.
- Add a section on reversibility of time series (cf: Diks,
Chapter 4).
- Mention maximally chaotic (largest
*D*_{KY}) jerk
system
in
section 5.9.
- Update list of journals with chaos and related papers in
Appendix C.
- Discuss autocorrelation function of 1/
*f *^{a}
noise.
- Discuss Milnor attractors (Comm. Math. Phys. 99, 177 (1985)).
- Give the transformation for the derivation of
*P*(*X*)
for
the
logistic
map (page 34).
- Show a graph of the LLE versus
*s* for a high-*D*
neural
network
(universal?) (page 141).
- Say more about generalized Lotka-Volterra models.
- Mention Misiurewicz
Points and snap-back repellors.
- Include a higher-resolution
version of Fig. 14.4.
- Mention the pinball machine as an example of transient chaos.
- Include photo of Galton board from Physics Museum in Chapter 1.
- Include photo of cream mixing with coffee in Chapter 1.

- Say more about labyrinth chaos and extensions to higher
dimensions.
- Discuss conditions for boundedness, inward flow on a large
hypersphere.
- Discuss methods for identifying multiple attractors and global
bifurcations.
- Add terms to the approximations in Appendix B.7 (see Clapham
and Nicholson).
- Plot Eq. (14.7) in Fig. 14.7.
- Add a figure showing the basins of attraction for Eq. (14.30).
- Discuss Sarkovskii's
theorem
- Report maximum LE
and Dky for the Henon map and other cases.
- Give a form of Eq. (5.30) valid for any dimension.
- Explain the Eq. (15.30), etc. use the approximations in Eq.
(9.38) - (9.42).
- Add the Fermi map.
- Remove or fix ill-posed exercises (see solutions
manual).
- Check all Sprott
papers published since 2003 for additional material.
- Add Aitken's method of extrapolation to Section 10.1