Estimating the dimension of the attractor for the complex Ginzburg-Landau system

Yu Yan; Shunqin Zhang; Xiaoling Zhang; Yu Yan; Shunqin Zhang; Xiaoling Zhang

doi:10.3934/era.2026022

Electronic Research Archive

2026, Volume 34, Issue 1: 463-476. doi: 10.3934/era.2026022

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Research article

Estimating the dimension of the attractor for the complex Ginzburg-Landau system

1.
School of Mathematics, Hohai University, Nanjing 210098, China
2.
Laboratory of Mathematical Modeling and Intelligent Computing for Water Systems, Hohai University, Nanjing 211100, China

Received: 01 October 2025 Revised: 24 December 2025 Accepted: 09 January 2026 Published: 15 January 2026

In this paper, the upper bound of the dimension of the global attractor associated with the four-dimensional cubic complex Ginzburg-Landau system is derived using the Lyapunov exponent method. First, by employing the Faedo-Galerkin method and energy estimation, the existence and uniqueness of solutions under the variational form of the system are established. Subsequently, a specific quantity is constructed and transformed into an inequality, from which the upper bound of the fractal dimension corresponding to the global attractor of the dynamical system is obtained.
- complex Ginzburg-Landau system,
- attractor,
- dimension estimation,
- Lyapunov exponent
Citation: Yu Yan, Shunqin Zhang, Xiaoling Zhang. Estimating the dimension of the attractor for the complex Ginzburg-Landau system[J]. Electronic Research Archive, 2026, 34(1): 463-476. doi: 10.3934/era.2026022

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Abstract

In this paper, the upper bound of the dimension of the global attractor associated with the four-dimensional cubic complex Ginzburg-Landau system is derived using the Lyapunov exponent method. First, by employing the Faedo-Galerkin method and energy estimation, the existence and uniqueness of solutions under the variational form of the system are established. Subsequently, a specific quantity is constructed and transformed into an inequality, from which the upper bound of the fractal dimension corresponding to the global attractor of the dynamical system is obtained.

References

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