Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29107
Title: Detection of chaos in some local regions of phase portraits using shannon entropies
Authors: Ling, BWK
Ho, CYF
Tam, PKS
Keywords: Second-order digital filter
Shannon entropy
Two's complement arithmetic
Issue Date: 2004
Publisher: World Scientific
Source: International journal of bifurcation and chaos in applied sciences and engineering, 2004, v. 14, no. 4, p. 1493-1499 How to cite?
Journal: International journal of bifurcation and chaos in applied sciences and engineering 
Abstract: This letter demonstrates the use of Shannon entropies to detect chaos exhibited in some local regions on the phase portraits. When both eigenvalues of the second-order digital filters with two's complement arithmetic are outside the unit circle, the Shannon entropies of the state variables are independent of the initial conditions and the filter parameters, except for some special values of the filter parameters. At these special values, the Shannon entropies of the state variables are relatively small. The state trajectories corresponding to these filter parameters either exhibit random-like chaotic behaviors in some local regions or converge to some fixed points on the phase portraits. Hence, by measuring the Shannon entropies of the state variables, these special state trajectory patterns can be detected. For completeness, we extend the investigation to the case when the eigenvalues of the second-order digital filters with two's complement arithmetic are complex and are inside or on the unit circle. It is found that the Shannon entropies of the symbolic sequences for the type II trajectories may be higher than that for the type III trajectories, even though the symbolic sequences of the type II trajectories are periodic and have limit cycle behaviors, while that of the type III trajectories are aperiodic and have chaotic behaviors.
URI: http://hdl.handle.net/10397/29107
ISSN: 0218-1274
EISSN: 1793-6551
DOI: 10.1142/S0218127404010023
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