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We have qualitatively analyzed different cases of human disorders and displacement activities of animals and hypothesize that some of them are examples of low-dimensional dynamical chaos in biological organisms. We also considered a biological organism in the framework of the control system theory and found that chaotic regime in one subsystem may be compensating for the loss of chaos in another subsystem for the sake of stability of the whole system. According to the hypothesis chaotic behavior of different organs sets in a human body as an alternative to serious diseases or even death. The principle of compensation was applied to different physiological systems with chaotic regimes to explain the adaptive nature of chaos there. Implications of the mechanism of adaptive chaos for sleep diseases, e.g., enuresis, and other potentially life threatening disorders of humans, e.g., RLS, are discussed in connection with the possibility to use these ideas for improved treatment strategies. The main conclusion is that adaptive disorders with chaotic symptoms should not be aggressively treated; if adaptive disorders are overtreated, the whole organism may be thrown into a more regular state, which eventually will lead to a chronic disease or even death.