Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.
A two-parameter continuation method was developed and shown in the form of an example, allowing determination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations were made for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the range of oscillation in the reactor was determined. The results were confirmed on the bifurcation diagram of steady states and on time charts. The method is universal and can be used for various models of chemical reactors.