Recently, for modeling biological amplification processes, nonlinear amplifiers based on the Andronov–Hopf bifurcation have become a focus of attention. In this contribution, we analyze discrete-time implementations of this type of amplifiers. The effects of the time-discretization by explicit integration methods are discussed. A novel discrete-time system based on the Neimark–Sacker bifurcation is introduced, that outstandingly approximates the behavior of a particular Hopf-type amplifier.

In this contribution, the limitations of the Carleman linearization approach are presented and discussed. The Carleman linearization transforms an ordinary nonlinear differential equation into an infinite system of linear differential equations which cannot be solved in general. Therefore, the infinite dimensional system has to be approximated by a finite one. The idea of this contribution is to use a Taylor series for the approximation of the infinite system.

Recently, nonlinear amplifiers based on the Andronov–Hopf bifurcation have become a focus of attention in modeling of the mammalian hearing organ. We present a flexible framework implemented on a DSP to analyze various bifurcation based amplifiers to get deeper insights in their nonlinear input-output behavior. A comparison shows the Neimark–Sacker amplifier remarkably outperforms the Andronov–Hopf amplifier regarding the CPU usage.