Resonance frequency equilibrium reactions

System (A8.2)-(A8.4) defines completely the time variation of orientation and angular velocity for every path X(t). One can easily see that (A8.2)-(A8.4) describe the system with parametrical modulation, as the X(t) variation is an input noise and does not depend on behaviour of the solution of (Q(t), co(r). In other words, the back reaction of the rotator to the collective motion of the closest neighbourhood is neglected. Since the spectrum of fluctuations X(t) does not possess a carrying frequency, in principle, for the rotator the conditions of parametrical resonance and excitation (unrestricted heating of rotational degrees of freedom) are always fulfilled. In reality the thermal equilibrium is provided by dissipation of rotational energy from the rotator to the environment and... 

For nonlinear reaction schemes, maintained far from chemical equilibrium, a variety of more interesting interactions are possible (2) These include threshold phenomena in which a small transitory external perturbation may induce a permanent change in the steady state concentrations of metabolites. In such a case the magnitude of the change may be independent of that of the stimulus beyond a certain threshold value. Nonlinear reactions may also display a form of resonance when the perturbation oscillates in time. This can be inferred by examining the stability properties of linearized forms of nonlinear reaction schemes (2, 3) A complete description of this form of interaction, however, usually requires numerical computations ( ). I shall now describe the results of some computations in which a nonlinear reaction scheme that is capable of autonomous oscillations was perturbed by an oscillating stimulus applied over a range of frequencies ( ) ... 

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