The digital acoustic model of a nuclear reactor (DAMNR) is presented as an auto-oscillatory system belonging to a special class of nonlinear dissipative systems capable of generating undamped oscillations. It is established that a water-water power reactor with a turbulent flow of a coolant is an open system of high complexity with a large number of elements, the connections between which are not predetermined, but probabilistic. Elements of the coolant circuit with negative dissipation (negative friction) are identified. It is shown that they self-organize chaotic turbulent pulsations and vortices into ordered wave oscillations, the frequency of which is determined by the Thomson (Kelvin) formula. In radio engineering circuits, an electronic self-oscillating generator with transformer feedback has similar properties. The presence of negative resistance in nonlinear dynamical systems leads to self-organization of chaotic turbulent perturbations and generation of self-oscillations in the form of acoustic standing waves (ASW). On the basis of theoretical and experimental data, the reliability of a previously unknown property of a reactor with connected pipelines - the ability to generate several ASW simultaneously-was confirmed. The use of DAMNR in the design and operation of nuclear power plants allows to identify the sources of ASW occurring in the coolant, the conditions for their occurrence and frequency.