Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 12.4, Problem 3E
Interpretation Introduction
Interpretation:
To obtain a long time series for x(t) and numerically integrate the Rössler system for a = 0.4, b = 2, c = 4. By the attractor reconstruction method, plot (x(t),x(t+τ)) for various values of the delay, and find the value of τ for which the reconstructed attractor looks similar to the actual Rössler attractor. Also, explain how τ is compared with the typical orbital periods of the system.
Concept Introduction:
The Rössler system is:
˙x=−y−z˙y=x+ay˙z=b+z(x−c)
In the attractor reconstruction method, the time delay τ is introduced by observing graphs, for which the value of τ the phase space looks similar to the actual Lorenz attractor.
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Chapter 12 Solutions
Nonlinear Dynamics and Chaos
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.2 - Prob. 1E
Ch. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5E
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