Dynamical systems design of nonlinear oscillators using phase reduction approach

In this paper, we present a dynamical systems design approach for nonlinear oscillators based on the phase reduction theory. Recently, design approaches of nonlinear circuits and devices focus on the mathematical structure of the target circuits and devices as dynamical systems. In general, the dynamical systems design approaches can be characterized by mathematical structures embedded into nonlinear circuits and devices. To clarify our standpoint, we classify such approaches into three: the phase plane and nullcline-based design, the potential-based design, and the phase response curve-based design. The distinct approaches can provide us with different perspectives in practical design. As a part of the dynamical systems design approaches, we propose a computer-aided phase reduction approach related with device macro modeling of nonlinear oscillators. Finally, we show several case studies by our approach and potential applications in biomedical engineering.