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Received: 5 Janurary 2020 Accepted: 7 March 2020 The purpose of this paper mainly explores the vibration resonance of the biological enzyme system with time delay, velocity feedback, and displacement feedback, under the excitation of signals with different frequencies and periods. Under approximate conditions, the fast and slow variables were separated to obtain the analytical solution of the system. the approach were theoretical analysis and numerical analysis show that the response amplitude gain of the biological enzyme system to low-frequency signal has two periodical relationships with the time delay: the period of low-frequency signal and that of high-frequency signal. The numerical results indicated that, the response amplitude gain is greatly affected by the symmetry and scale of the amplitudes, displacement response strengths, velocity response strengths of lowand high-frequency signals. For example, when the nonlinear term of the system μ=0.001, the response amplitude gain Q first increases, then decrease, and finally rebounds, with the growth of the frequency f of lowfrequency signal; when μ=0, Q increases significantly with the growth of f, and the increasing rate grows proportionally; When the strength of displacement feedback u=0.08 and that of velocity feedback v=0.01 (that is, u and v are unequal), the change scope of amplitude gain Q widens. The research results shed important new light on vibration resonance of biological enzyme systems.

Response Features of Biological Enzyme System to Excitation Signals of Different Frequencies and Periods