Transition to Chaos: From Small to Large Systems in the Nikolaevskiy Model

DOI10.1142/S0218127420300025zbMath1432.35116OpenAlexW3006635644MaRDI QIDQ5220431

Simon Hartmann, Steffen Richters-Finger, Stefan J. Linz

Publication date: 23 March 2020

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127420300025

zbMATH Keywords

transition to chaosNikolaevskiy equationsmall system limit

Mathematics Subject Classification ID

Attractors (35B41) Pattern formations in context of PDEs (35B36) Higher-order parabolic systems (35K41)

Cites Work

• Unnamed Item
• Exponential time differencing for stiff systems
• Determining Lyapunov exponents from a time series
• The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems
• Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
• A model for nonlinear seismic waves in a medium with instability
• On the nature of turbulence
• Pattern Formation
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
• Amplitude Equation of Higher-Dimensional Nikolaevskii Turbulence
• Fourth-Order Time-Stepping for Stiff PDEs
• Pattern formation outside of equilibrium
• Continuum modeling of particle redeposition during ion-beam erosion. Continuum modeling of particle redeposition during ion-beam erosion, one-dimensional case