Devaney chaos in high-dimensional linear fourth-order PDE
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Pengxian Zhu [1] ; Qiaomin Xiang [2]
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[1] Zhongkai University of Agriculture and Engineering
Zhongkai University of Agriculture and Engineering
China
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[2] Foshan University
Foshan University
China
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
- Idioma: inglés
- Enlaces
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Resumen
This paper focuses on a linear partial differential equation (PDE) with a fourth-order time derivative and high-dimensional spatial variables. Its high-dimensionality and higher-order properties pose challenges for investigating chaotic dynamics in this PDE. Taking the correlation of dynamical behaviors with coefficients as an entry point, we conduct a systematic exploration of the explicit relationship between chaotic behavior and the coefficient discriminant. Analysis demonstrates that when the coefficient discriminant is positive, this PDE exhibits Devaney chaos. Conversely, a non-positive discriminant indicates stability. This research approach enables the rapid determination of whether chaos exists through coefficients.
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