Difficulties in detecting chaos in a complex system

• Published in: Applied mathematics and computation Vol. 260; pp. 35 - 47
• Main Author: Petkov, Boyan H.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2015
• Subjects: Complex chaotic systems; Correlation dimension; Detection of chaos; Embedding dimension; Lyapunov exponents; Complex chaotic systems; Embedding dimension; Detection of chaos; Lyapunov exponents; Correlation dimension
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2015.03.034

•Analysis of the all sequences generated by a 7D map.•Application of the widely used methods detecting chaos in the real world.•Evaluation of the invariants of the reconstructed attractors.•Comparison of the results with those obtained for a 3D map.•Results indicate some difficulties in detecting chaos in the 7D map. The sequences, given by a 7D map, are analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system, determined by comparatively high number of parameters. The same diagnostic approaches are applied to the 3D Lorenz map for comparison. The results show that for some of the sequences yielded from the 7D map, the adopted methods are not able to give astraightforward answer to the question if the system is chaotic as in the 3D case. Since the sequences, subject to the analysis, are not contaminated by noise and are sufficiently long, it could be assumed that such difficulties arise likely due to specific internal features of the more complex system. It is found also that an increase from 0.01 to 0.5 of the sampling step, determining the sequences obtained from the 7D map, masks the chaos in some of them.