Self-oscillatory phenomenon

L. Mandelstam and N. Papalexi performed an interesting experiment of this kind with an electrical oscillatory circuit. If one of the parameters (C or L) is made to oscillate with frequency 2/, the system becomes self-excited with frequency/ this is due to the fact that there are always small residual charges in the condenser, which are sufficient to produce the cumulative phenomenon of self-excitation. It was found that in the case of a linear oscillatory circuit the voltage builds up beyond any limit until the insulation is ultimately punctured if, however, the system is nonlinear, the amplitude reaches a stable stationary value and oscillation acquires a periodic character. In Section 6.23 these two cases are represented by the differential equations (6-126) and (6-127) and the explanation is given in terms of their integration by the stroboscopic method. 

Non-equilibrium soft matter is an emerging research field, which could be able to explain a range of phenomenon of self-organization by association of reaction-diffusion mechanism and phase separations. Those phenomena are necessary for preparation of new materials of specific applications and can have possible relevance in the synthetic nanodevices. Thus, applications of the oscillatory chemical reaction continue to grow with rapid progress of nonlinear science. 

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