Search

We propose a method for designing 2-D limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly perturbed limit-cycle oscillators and is widely used in the analysis of synchronization dynamics. We develop an algorithm for designing the vector field with a stable limit cycle that possesses a given shape and also a given phase sensitivity function. The vector field of the limit-cycle oscillator is approximated by polynomials whose coefficients are estimated by convex optimization. The linear stability of the limit cycle is ensured by introducing an upper bound to the Floquet exponent. The validity of the proposed method is verified numerically by designing several types of 2-D existing and artificial oscillators. As applications, we first design a limit-cycle oscillator with an artificial star-shaped periodic trajectory and demonstrate global entrainment. We then design a limit-cycle oscillator with an artificial high-harmonic phase sensitivity function and demonstrate multistable entrainment caused by a high-frequency periodic input.

A novel method to identify accurate polarization characteristics for concentration dependent electrochemical reaction was developed. This method identifies polarization characteristics which is dependent of concentration on electrode surface of flow cell. Since the concentration on the electrode surface sitting in a flow cell cannot be measured directly, inverse analysis approach is applied. As the observation information of this inverse problem, total currents on the electrode are measured with different bulk concentration. The unknown polarization characteristics are expressed with piecewise linear function with unknown parameters. The relationship between observation and unknown parameters are modeled with advection-diffusion equation. The fluid velocity field of the flow cell is modeled with Navier-Stokes equation. These equations are discretized by finite volume method. In order to validate the proposed method, identification using both numerically generated data and experimental data were performed. The validation result demonstrated the good accuracy of the method.