On the Chaotic Dynamics Associated with the Center Manifold Equations of Double-Diffusive Convection Near a Codimension-Four Bifurcation Point at Moderate Thermal Rayleigh Number
| Autor: | Jerry F. Magnan, Justin S. Eilertsen |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Convection Applied Mathematics 010102 general mathematics Mathematical analysis Rayleigh number Codimension 01 natural sciences 010305 fluids & plasmas Nonlinear Sciences::Chaotic Dynamics Bifurcation theory Modeling and Simulation 0103 physical sciences Thermal 0101 mathematics Engineering (miscellaneous) Center manifold Double diffusive convection Poincaré map |
| Zdroj: | International Journal of Bifurcation and Chaos. 28:1850094 |
| ISSN: | 1793-6551 0218-1274 |
| DOI: | 10.1142/s0218127418500943 |
| Popis: | We analyze the dynamics of the Poincaré map associated with the center manifold equations of double-diffusive thermosolutal convection near a codimension-four bifurcation point when the values of the thermal and solute Rayleigh numbers, [Formula: see text] and [Formula: see text], are comparable. We find that the bifurcation sequence of the Poincaré map is analogous to that of the (continuous) Lorenz equations. Chaotic solutions are found, and the emergence of strange attractors is shown to occur via three different routes: (1) a discrete Lorenz-like attractor of the three-dimensional Poincaré map of the four-dimensional center manifold equations that forms as the result of a quasi-periodic homoclinic explosion; (2) chaos that follows quasi-periodic intermittency occurring near saddle-node bifurcations of tori; and, (3) chaos that emerges from the destruction of a 2-torus, preceded by frequency locking. |
| Databáze: | OpenAIRE |
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