We describe the implementation of a new laboratory-based interdisciplinary undergraduate course on nonlinear dynamical systems. Geometrical methods and data visualization techniques are especially emphasized. A novel feature of the course is a required laboratory where the students analyze the behavior of a number of dynamical systems. Most of the laboratory experiments can be economically implemented using equipment available in many introductory physics microcomputer-based laboratories.
REFERENCES
1.
S. H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering (Addison–Wesley, Reading, MA, 1994).
2.
R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (Oxford U.P., New York, 1994).
3.
Robert C.
Hilborn
and Nicholas B.
Tufillaro
, “Resource Letter ND-1: Nonlinear Dynamics
,” Am. J. Phys.
65
, 822
–834
(1997
).4.
W. Lauterborn, T. Kurz, and M. Wiesenfeldt, Coherent Optics: Fundamentals and Applications (Springer, New York, 1995), Chap. 10.
5.
J. D. Murray, Mathematical Biology (Springer Verlag, New York, 1993).
6.
H. Gollwitzer, DIFFERENTIAL SYSTEMS 4.0 (U’Betcha Publications, 554 Evans Road, Springfield, PA 19064, 1996); (610) 544-9257, hgollwit@mcs.drexel.edu
7.
MATLAB 5.2 available from The Mathworks, Inc., 24 Prime Park Way, Natick, MA 01760; (508) 647-7000, http://www.mathworks.com
8.
The Universal Laboratory Interface (ULI) boxes are available from Vernier Software and Technology (www.vernier.com). Tel: (503) 277-2299. This company also supplies probes for temperature, current and voltage, force, motion (both linear and rotational) and Data transfer was via a number of Vernier software packages including DATALOGGER, MACMOTION, ELECTRICITY, and ULITIMER.
9.
G.
Fletcher
, “A mechanical model of first- and second-order phase transitions
,” Am. J. Phys.
65
, 74
–81
(1997
).10.
R. V.
Mancuso
, “A working mechanical model for the first- and second-order phase transitions and the cusp catastrophe
,” Am. J. Phys.
68
, 271
–277
(2000
).11.
S. R. Bishop and M. S. Soliman, “The prediction of ship capsize: Not all fractals are environment friendly,” in Application of Fractals and Chaos, edited by Crilly, Earnshaw, and Jones (Springer-Verlag, New York, 1993).
12.
K.
Briggs
, “Simple experiments in chaotic dynamics
,” Am. J. Phys.
55
, 1083
–1089
(1987
).13.
K.
Dreyer
and F. R.
Hickey
, “The route to chaos in a dripping water faucet
,” Am. J. Phys.
59
, 619
–627
(1991
).14.
J. E.
Berger
and G.
Nunes
, “A mechanical Duffing oscillator for the undergraduate laboratory
,” Am. J. Phys.
65
, 841
–846
(1997
).15.
Earle S. Scott, Rodney Schreiner, Lee R. Sharpe, Bassam Z. Shakhashiri, and Glen E. Dirreen, “Oscillating Chemical Reactions,” in Chemical Demonstrations, edited by B. Z. Shakhashiri (University of Wisconsin Press, Madison, WI, 1985), Vol. 2, Chap. 7.
16.
T.
Shinbrot
, C.
Grebogi
, J.
Wisdom
, and J. A.
Yorke
, “Chaos in a double pendulum
,” Am. J. Phys.
60
, 491
–499
(1992
).17.
R. B.
Levien
and S. M.
Tan
, “Double pendulum: An experiment in chaos
,” Am. J. Phys.
61
, 1038
–1044
(1993
).18.
J. A.
Campbell
, “Beating Heart
,” J. Chem. Educ.
34
, A105
(1957
), and also see the letter on p. 362.19.
M. P.
Kennedy
, “Three Steps to Chaos. I Evolution
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
40
(10
), 640
–656
(1993
);M. P.
Kennedy
, “Three Steps to Chaos. II A Chua’s Circuit Primer
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
40
, 657
–674
(1993
).20.
S. J.
Van Hook
and M. F.
Schatz
, “Simple demonstrations of pattern-formation
,” Phys. Teach.
35
, 391
–395
(1997
).
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© 2001 American Association of Physics Teachers.
2001
American Association of Physics Teachers
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