A Programmable On-Chip Hopf Bifurcation Circuit

Abstract

This effort discusses a programmable Hopf bifurcation element based on Transconductance Amplifiers (TA) that can be directly implemented in configurable hardware (e.g. an SoC FPAA). The TA Hopf bifurcation circuit shows the complete dynamics of a Van der Pol circuit, a Hopf bifurcation prototype. This Low-Pass Filter (LPF) TA-implemented ODE shows the necessary linear dynamics, as well as stable and oscillatory nonlinear dynamics expected near a Hopf bifurcation. This component directly uses the dynamics of the TA devices not translating equations, reducing the implementation complexity.