Encoding information using OAM beams as carriers greatly alleviates the capacity crisis in communication systems. When transmitted through the atmospheric channel, OAM beams are influenced by the random fluctuations in the refractive index caused by atmospheric turbulence, resulting in phase distortion and intensity dispersion of the beams, leading to severe signal interference. Due to the high randomness of atmospheric turbulence, it is essential for OAM mode recognition methods to have good stability to ensure communication quality. We establish an equivalence relationship between the continuous dynamics system and the network unit RUEM, ensuring its stability through theoretical derivation and numerical experiments. We propose a multitask neural network model, OATNN, embedded with RUEM to achieve efficient simultaneous recognition of turbulence intensity in atmospheric turbulence environments and OAM modes in free-space optical communication systems. Numerical experimental results show that under four turbulence intensity levels, the network achieves a recognition accuracy of 99.37%, and for ten modes, the recognition accuracy is 99.05%. Additionally, we explore the performance of this network in a 2000m channel transmission scenario.
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