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

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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.

Keywords

complex Ginzburg-Landau system / attractor / dimension estimation / Lyapunov exponent

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