scholarly journals Analytical prediction of the transition to chaos in Lorenz equations

2010 ◽  
Vol 23 (5) ◽  
pp. 503-507 ◽  
Author(s):  
Peter Vadasz
Author(s):  
Peter Vadasz

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.


Author(s):  
Peter Vadasz

The failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in porous media natural convection 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.


1997 ◽  
Vol 7 (6) ◽  
pp. 603-616 ◽  
Author(s):  
David P. Schmidt ◽  
Michael L. Corradini

1982 ◽  
Vol 12 (3) ◽  
pp. 279-288 ◽  
Author(s):  
T. A. Carroll ◽  
R. D. Noble ◽  
R. G. Buschman

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Gang Lu ◽  
Ritske S. Huismans

AbstractBreakup volcanism along rifted passive margins is highly variable in time and space. The factors controlling magmatic activity during continental rifting and breakup are not resolved and controversial. Here we use numerical models to investigate melt generation at rifted margins with contrasting rifting styles corresponding to those observed in natural systems. Our results demonstrate a surprising correlation of enhanced magmatism with margin width. This relationship is explained by depth-dependent extension, during which the lithospheric mantle ruptures earlier than the crust, and is confirmed by a semi-analytical prediction of melt volume over margin width. The results presented here show that the effect of increased mantle temperature at wide volcanic margins is likely over-estimated, and demonstrate that the large volumes of magmatism at volcanic rifted margin can be explained by depth-dependent extension and very moderate excess mantle potential temperature in the order of 50–80 °C, significantly smaller than previously suggested.


2021 ◽  
Vol 62 ◽  
pp. 37-46
Author(s):  
Wei Bai ◽  
Anish Roy ◽  
Lingxi Guo ◽  
Jianfeng Xu ◽  
Vadim V. Silberschmidt

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