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IJBC
2007

Extended Phase Diagram of the Lorenz Model

9 years 5 months ago
Extended Phase Diagram of the Lorenz Model
The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-B´enard flow is studied. Its bifurcation structure has commonly been investigated as a function of r, the normalized Rayleigh number, at fixed Prandtl number σ. The present work extends the analysis to the entire (r, σ) parameter plane. An onion like periodic pattern is found which is due to the alternating stability of symmetric and non-symmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and σ. In addition to the limit which was previously analyzed by Sparrow, we identify two more distinct asymptotic regimes in which either σ/r or σ2/r is constant. In both limits the dynamics is approximately described by Airy functions whence the periodicity in parameter space can be calculated analytically. Furthermore, some observations about sequences of bifurcations and coexistence of ...
H. R. Dullin, S. Schmidt, P. H. Richter, S. K. Gro
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2007
Where IJBC
Authors H. R. Dullin, S. Schmidt, P. H. Richter, S. K. Grossmann
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