“Oscillator–wave” model: properties and heuristic instances

The article considers a generalized model of an oscillator, subjected to the influence of an external wave. It is shown that the systems of diverse physical background, which this model encompasses by their nature, should belong to the broader, proposed in previous works class of “kick-excited self-adaptive dynamical systems”. The theoretical treatment includes an analytic approach to the conditions for emergence of small and large amplitudes, i.e. weak and strong non-linearity of the system. Derived also are generalized conditions for the transition of systems of this “oscillator–wave” type to non-regular and chaotic behaviour. For the purpose of demonstrating the heuristic properties of the generalized oscillator–wave model from this point of view are considered the relevant systems and phenomena of the quantized cyclotron resonance and the megaquantum resonance-wave model of the Solar System. We point to a number of other natural and scientific phenomena, which can be effectively analyzed from the point of view of the developed approach. In particular we stress on the possibility for development and the wide applicability of specific wave influences, for example for the improvement and the speeding up of technological processes.