A search for the simplest chaotic partial differential equation

DOI10.1016/j.physleta.2009.05.050zbMath1232.35034OpenAlexW2121163753WikidataQ115341615 ScholiaQ115341615MaRDI QIDQ663035

Charles D. Brummitt, Julien Clinton Sprott

Publication date: 13 February 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2009.05.050

zbMATH Keywords

chaospartial differential equationstrange attractor

Mathematics Subject Classification ID

Nonlinear higher-order PDEs (35G20) Free boundary problems for PDEs (35R35) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Cyclic vectors, hypercyclic and chaotic operators (47A16)

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Dynamical features of the generalized Kuramoto-Sivashinsky equation ⋮ Least squares shadowing sensitivity analysis of a modified Kuramoto-Sivashinsky equation ⋮ Approximation error approach in spatiotemporally chaotic models with application to Kuramoto-Sivashinsky equation ⋮ A New Chaotic Attractor Around a Pre-Located Ring ⋮ A Tribute to J. C. Sprott ⋮ Unnamed Item ⋮ Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks ⋮ Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system ⋮ Takagi-Sugeno fuzzy modeling and chaos control of partial differential systems

Cites Work

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• Simplest dissipative chaotic flow.
• An equation for continuous chaos
• Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
• Non-chaotic behaviour in three-dimensional quadratic systems
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• Deterministic Nonperiodic Flow

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