Hopf bifurcation and strange attractors in Chebyshev spectral solutions of the Burgers equation

DOI10.1016/0096-3003(94)00242-8zbMath0844.65074OpenAlexW2062483422MaRDI QIDQ1908237

H. Dang-Vu, C. Delcarte

Publication date: 29 August 1996

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(94)00242-8

zbMATH Keywords

stabilitystrange attractorslimit cyclesBurgers equationHopf bifurcationAdams-Moulton methodChebyshev pseudospectral collocation methodChebyshev tau spectral method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (3)

Dynamics in spectral solutions of Burgers equation ⋮ Dynamics and synchronization of numerical solutions of the Burgers equation ⋮ Formations of Transitional Zones in Shock Wave with Saddle-Node Bifurcations

Cites Work

• Determining Lyapunov exponents from a time series
• An accurate solution of the Poisson equation by the Chebyshev collocation metod
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• A five-dimensional truncation of the plane incompressible Navier-Stokes equations
• Note concerning our paper On the nature of turbulence. Commun. math. Phys. 20, 167-192 (1971)
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