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The adaptation of systems to external influences is of broad interest. We study the influence of microwave signals of different shapes on the magnetoacoustic wave system with a giant nonlinearity in canted antiferromagnet FeBO₃ at room temperature, which is close to its phase transition to the paramagnetic state. The classical nonlinear system obeys external deterministic signals; the modulation response describes the shape of these signals. In response to a noisy spectrum, the system shows self-organization, and mode competition selects one excited mode while suppressing others. With an increase in the power of the external signal, another self-organization is observed in the form of a narrow peak at the frequency of the fundamental minimum. This represents the first observation of the macroscopic quantum statistical phenomenon, Bose-Einstein condensation of magnetoacoustic wave quanta in a wave system with a high level of thermal fluctuations. The resulting picture of adaptation can analogously be transferred to many other adaptive wave systems, including large scale adaptive wave systems in the natural environment.