Detecting the phenomenon of strange non-chaotic attractors

Alan Oxley

Abstract


I comment on how chaos might be defined. A sample of dynamical systems that have quasi-periodic forcing functions is then considered. The normal approach found in the literature is to start with an ordinary differential equation, change to a difference equation, and then plot a graph. The question of how to detect a strange non-chaotic attractor without the underlying ordinary differential equation is posed and some pointers are given as to a possible method of solution using statistical analysis.

References
  • Banks J., Brooks J., Cairns G., Davis G. and Stacey P., On Devaney's definition of chaos, American Mathematics Monthly. 99 (1992), 332--334.
  • Box G. E. P, Jenkins G. M. and Reinsel G. C., Time series analysis John Wiley and Sons, New Jersy, 2008.
  • Feitelson D. G., Workload modeling for performance evaluation, In: Lecture notes in computer science, vol. 2459, Springer, Berlin, 2002, 114--141.
  • Glendinning P., The nonsmooth pitchfork bifurcation, Discrete and Continuous Dynamical Systems B. 4 (2004), 457--464.
  • Glendinning P., T. H. Jager and G. Keller, How chaotic are strange non-chaotic attractors?, Nonlinearity. 19 (2006), 2005--2022.
  • Glendinning P., View from the Pennines: strange nonchaotic attractors, Mathematics Today. 44 (2008), 119--120.
  • Keller G., A note on strange nonchaotic attractors, Fundamenta Mathematicae. 151 (1996), 139--148.
  • Li H., Workload dynamics on clusters and grids, Journal of Supercomputing. 47) (2009), 1--20.
  • Lublin U., Feitelson D. G., The workload of parallel supercomputers: modeling the characteristics of rigid jobs, J. Parallel Distrib Comput. 63(11) (2003), 1105--1122.
  • Squillante M. S., Yao D. D and Zhang L. The impact of job arrival patterns on parallel scheduling, ACM SIGMETRICS Perform Eval Rev. 26(4) (1999), 52--59.

Keywords


Dynamical systems, SNA, chaotic dynamics, difference equations, quasi-periodically forced oscillators, periodic forcing.

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DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2454



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