Analytical prediction of the transition to chaos in Lorenz system

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in Lorenz equations motivates this study. A weak non-linear solution to the problem is shown to produce an accurate analytical expression for the transition point as long as the validity condition and consequent accuracy of the latter solution is fulfilled. The analytical results are compared to accurate computational solutions showing an excellent fit within the validity domain of the analytical solution.

Original languageEnglish (US)
Title of host publication2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis
Pages799-803
Number of pages5
Volume2
StatePublished - 2009
Event2008 9th Biennial Conference on Engineering Systems Design and Analysis - Haifa, Israel
Duration: Jul 7 2008Jul 9 2008

Other

Other2008 9th Biennial Conference on Engineering Systems Design and Analysis
CountryIsrael
CityHaifa
Period7/7/087/9/08

Fingerprint

Chaos theory
Linear stability analysis

ASJC Scopus subject areas

  • Computational Mechanics
  • Control and Systems Engineering
  • Mechanical Engineering

Cite this

Vadasz, P. (2009). Analytical prediction of the transition to chaos in Lorenz system. In 2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis (Vol. 2, pp. 799-803)

Analytical prediction of the transition to chaos in Lorenz system. / Vadasz, Peter.

2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis. Vol. 2 2009. p. 799-803.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Vadasz, P 2009, Analytical prediction of the transition to chaos in Lorenz system. in 2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis. vol. 2, pp. 799-803, 2008 9th Biennial Conference on Engineering Systems Design and Analysis, Haifa, Israel, 7/7/08.
Vadasz P. Analytical prediction of the transition to chaos in Lorenz system. In 2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis. Vol. 2. 2009. p. 799-803
Vadasz, Peter. / Analytical prediction of the transition to chaos in Lorenz system. 2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis. Vol. 2 2009. pp. 799-803
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