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Minimal chaotic models from the Volterra gyrostat

Seshadri, AK and Lakshmivarahan, S (2023) Minimal chaotic models from the Volterra gyrostat. In: Physica D: Nonlinear Phenomena, 456 .

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Official URL: https://doi.org/10.1016/j.physd.2023.133948


Low-order models obtained through Galerkin projection of several physically important systems (e.g., Rayleigh–Bénard convection, mid-latitude quasi-geostrophic dynamics, and vorticity dynamics) appear in the form of coupled gyrostats. Forced dissipative chaos is an important phenomenon in these models, and this paper introduces and identifies “minimal chaotic models” (MCMs), in the sense of having the fewest external forcing and linear dissipation terms, for the class of models arising from an underlying gyrostat core. The identification of MCMs reveals common conditions for chaos across a wide variety of physical systems. It is shown here that a critical distinction is whether the gyrostat core (without forcing or dissipation) conserves energy, depending on whether the sum of the quadratic coefficients is zero. The paper demonstrates that, for the energy-conserving condition of the gyrostat core, the requirement of a characteristic pair of fixed points that repel the chaotic flow dictates placement of forcing and dissipation in the minimal chaotic models. In contrast if the core does not conserve energy, the forcing can be arranged in additional ways for chaos to appear in the subclasses where linear feedbacks render fewer invariants in the gyrostat core. In all cases, the linear mode must experience dissipation for chaos to arise. The Volterra gyrostat presents a clear example where the arrangement of fixed points circumscribes more complex dynamics. © 2023 Elsevier B.V.

Item Type: Journal Article
Publication: Physica D: Nonlinear Phenomena
Publisher: Elsevier B.V.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Dynamics; Galerkin methods; Natural convection, Chaotic model; Forced-dissipative chaos; Forcings; Galerkin projections; Gyrostats; Low-order modeling; Lower order models; Minimal chaotic model; Volterra; Volterrum gyrostat, Energy conservation
Department/Centre: Division of Mechanical Sciences > Divecha Centre for Climate Change
Division of Mechanical Sciences > Centre for Atmospheric & Oceanic Sciences
Date Deposited: 01 Dec 2023 03:24
Last Modified: 01 Dec 2023 03:24
URI: https://eprints.iisc.ac.in/id/eprint/83338

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