Analytical prediction of the transition to chaos in Lorenz equations

Peter Vadasz

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The apparent 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 condition of validity 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)
Pages (from-to)503-507
Number of pages5
JournalApplied Mathematics Letters
Issue number5
StatePublished - May 2010


  • Analytical solution
  • Chaos
  • Lorenz equations
  • Transition to chaos

ASJC Scopus subject areas

  • Applied Mathematics


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