- Dowell, E.H. and Murphy, K.D. and Latz, A.L., Simplified predictive criteria for the onset of Chaos,
Nonlinear Dynamics, vol. 6 no. 3
pp. 247 - 263 .
(last updated on 2007/04/10)
Two alternative criteria for predicting the onset of chaos are presented. Both are based on the notion that it is the interaction between a stable and nearby unstable limit cycle pair in the phase space that disrupts the stable motion, thereby producing chaotic behavior. The first criterion is based upon an intersection of the unstable and stable limit cycle orbits in the phase plane. The second criterion proposes that an energy equivalence between the stable and unstable limitcycles may be responsible for the loss of periodicity of the stable motion. Both criteria are tested numerically using three distinct softening spring oscillators and their predictive capabilities are discussed. The results of this study, particularly for the energy criterion, are encouraging.
Forecasting;Phase space methods;Stability;Oscillators (mechanical);Heuristic methods;Oscillations;Differential equations;Mathematical models;