Multimode fibers (MMFs) support abundant spatial modes and involve rich spatiotemporal dynamics, yielding many promising applications. Here, we investigate the influences of the number and initial energy of high-order modes (HOMs) on the energy flow from the intermediate modes (IMs) to the fundamental mode (FM) and HOMs. It is quite surprising that random distribution of high-order modes evolves to a stationary one, indicating the asymptotic behavior of orbits in the same attraction domain. By employing the Lyapunov exponent, we prove that the threshold of the HOMs-attractor is consistent with the transition point of the energy flow which indiactes the HOMs-attracotr acts as a valve in the modal energy flow. Our results provide a new perspective to explore the nonlinear phenomena in MMFs, such as Kerr self-cleaning, and may pave the way to some potential applications, such as secure communications in MMFs.
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